How do I remove all null and empty string values from an object?

You're deleting sjonObj.key, literally. You need to use array access notation:

delete sjonObj[key];

However, that will also delete where value is equal to 0, since you're not using strict comparison. Use === instead:

$.each(sjonObj, function(key, value){
    if (value === "" || value === null){
        delete sjonObj[key];
    }
});

However, this will only walk the object shallowly. To do it deeply, you can use recursion:

(function filter(obj) {
    $.each(obj, function(key, value){
        if (value === "" || value === null){
            delete obj[key];
        } else if (Object.prototype.toString.call(value) === '[object Object]') {
            filter(value);
        } else if ($.isArray(value)) {
            $.each(value, function (k,v) { filter(v); });
        }
    });
})(sjonObj);

var sjonObj = {
  "executionMode": "SEQUENTIAL",
  "coreTEEVersion": "3.3.1.4_RC8",
  "testSuiteId": "yyy",
  "testSuiteFormatVersion": "1.0.0.0",
  "testStatus": "IDLE",
  "reportPath": "",
  "startTime": 0,
  "durationBetweenTestCases": 20,
  "endTime": 0,
  "lastExecutedTestCaseId": 0,
  "repeatCount": 0,
  "retryCount": 0,
  "fixedTimeSyncSupported": false,
  "totalRepeatCount": 0,
  "totalRetryCount": 0,
  "summaryReportRequired": "true",
  "postConditionExecution": "ON_SUCCESS",
  "testCaseList": [
    {
      "executionMode": "SEQUENTIAL",
      "commandList": [
        
      ],
      "testCaseList": [
        
      ],
      "testStatus": "IDLE",
      "boundTimeDurationForExecution": 0,
      "startTime": 0,
      "endTime": 0,
      "label": null,
      "repeatCount": 0,
      "retryCount": 0,
      "totalRepeatCount": 0,
      "totalRetryCount": 0,
      "testCaseId": "a",
      "summaryReportRequired": "false",
      "postConditionExecution": "ON_SUCCESS"
    },
    {
      "executionMode": "SEQUENTIAL",
      "commandList": [
        
      ],
      "testCaseList": [
        {
          "executionMode": "SEQUENTIAL",
          "commandList": [
            {
              "commandParameters": {
                "serverAddress": "www.ggp.com",
                "echoRequestCount": "",
                "sendPacketSize": "",
                "interval": "",
                "ttl": "",
                "addFullDataInReport": "True",
                "maxRTT": "",
                "failOnTargetHostUnreachable": "True",
                "failOnTargetHostUnreachableCount": "",
                "initialDelay": "",
                "commandTimeout": "",
                "testDuration": ""
              },
              "commandName": "Ping",
              "testStatus": "IDLE",
              "label": "",
              "reportFileName": "tc_2-tc_1-cmd_1_Ping",
              "endTime": 0,
              "startTime": 0,
              "repeatCount": 0,
              "retryCount": 0,
              "totalRepeatCount": 0,
              "totalRetryCount": 0,
              "postConditionExecution": "ON_SUCCESS",
              "detailReportRequired": "true",
              "summaryReportRequired": "true"
            }
          ],
          "testCaseList": [
            
          ],
          "testStatus": "IDLE",
          "boundTimeDurationForExecution": 0,
          "startTime": 0,
          "endTime": 0,
          "label": null,
          "repeatCount": 0,
          "retryCount": 0,
          "totalRepeatCount": 0,
          "totalRetryCount": 0,
          "testCaseId": "dd",
          "summaryReportRequired": "false",
          "postConditionExecution": "ON_SUCCESS"
        }
      ],
      "testStatus": "IDLE",
      "boundTimeDurationForExecution": 0,
      "startTime": 0,
      "endTime": 0,
      "label": null,
      "repeatCount": 0,
      "retryCount": 0,
      "totalRepeatCount": 0,
      "totalRetryCount": 0,
      "testCaseId": "b",
      "summaryReportRequired": "false",
      "postConditionExecution": "ON_SUCCESS"
    }
  ]
};

(function filter(obj) {
    $.each(obj, function(key, value){
        if (value === "" || value === null){
            delete obj[key];
        } else if (Object.prototype.toString.call(value) === '[object Object]') {
            filter(value);
        } else if (Array.isArray(value)) {
            value.forEach(function (el) { filter(el); });
        }
    });
})(sjonObj);

console.log(sjonObj)
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

Note that if you're willing to use a library like lodash/underscore.js, you can use _.pick instead. However, you will still need to use recursion to filter deeply, since neither library provides a deep filter function.

sjonObj = (function filter(obj) {
    var filtered = _.pick(obj, function (v) { return v !== '' && v !== null; });
    return _.cloneDeep(filtered, function (v) { return v !== filtered && _.isPlainObject(v) ? filter(v) : undefined; });
})(sjonObj);

This variant has the added advantage of leaving the original object unmodified, but it does create an entirely new copy, which would be less efficient if you don't need the original object.

var sjonObj = {
  "executionMode": "SEQUENTIAL",
  "coreTEEVersion": "3.3.1.4_RC8",
  "testSuiteId": "yyy",
  "testSuiteFormatVersion": "1.0.0.0",
  "testStatus": "IDLE",
  "reportPath": "",
  "startTime": 0,
  "durationBetweenTestCases": 20,
  "endTime": 0,
  "lastExecutedTestCaseId": 0,
  "repeatCount": 0,
  "retryCount": 0,
  "fixedTimeSyncSupported": false,
  "totalRepeatCount": 0,
  "totalRetryCount": 0,
  "summaryReportRequired": "true",
  "postConditionExecution": "ON_SUCCESS",
  "testCaseList": [
    {
      "executionMode": "SEQUENTIAL",
      "commandList": [
        
      ],
      "testCaseList": [
        
      ],
      "testStatus": "IDLE",
      "boundTimeDurationForExecution": 0,
      "startTime": 0,
      "endTime": 0,
      "label": null,
      "repeatCount": 0,
      "retryCount": 0,
      "totalRepeatCount": 0,
      "totalRetryCount": 0,
      "testCaseId": "a",
      "summaryReportRequired": "false",
      "postConditionExecution": "ON_SUCCESS"
    },
    {
      "executionMode": "SEQUENTIAL",
      "commandList": [
        
      ],
      "testCaseList": [
        {
          "executionMode": "SEQUENTIAL",
          "commandList": [
            {
              "commandParameters": {
                "serverAddress": "www.ggp.com",
                "echoRequestCount": "",
                "sendPacketSize": "",
                "interval": "",
                "ttl": "",
                "addFullDataInReport": "True",
                "maxRTT": "",
                "failOnTargetHostUnreachable": "True",
                "failOnTargetHostUnreachableCount": "",
                "initialDelay": "",
                "commandTimeout": "",
                "testDuration": ""
              },
              "commandName": "Ping",
              "testStatus": "IDLE",
              "label": "",
              "reportFileName": "tc_2-tc_1-cmd_1_Ping",
              "endTime": 0,
              "startTime": 0,
              "repeatCount": 0,
              "retryCount": 0,
              "totalRepeatCount": 0,
              "totalRetryCount": 0,
              "postConditionExecution": "ON_SUCCESS",
              "detailReportRequired": "true",
              "summaryReportRequired": "true"
            }
          ],
          "testCaseList": [
            
          ],
          "testStatus": "IDLE",
          "boundTimeDurationForExecution": 0,
          "startTime": 0,
          "endTime": 0,
          "label": null,
          "repeatCount": 0,
          "retryCount": 0,
          "totalRepeatCount": 0,
          "totalRetryCount": 0,
          "testCaseId": "dd",
          "summaryReportRequired": "false",
          "postConditionExecution": "ON_SUCCESS"
        }
      ],
      "testStatus": "IDLE",
      "boundTimeDurationForExecution": 0,
      "startTime": 0,
      "endTime": 0,
      "label": null,
      "repeatCount": 0,
      "retryCount": 0,
      "totalRepeatCount": 0,
      "totalRetryCount": 0,
      "testCaseId": "b",
      "summaryReportRequired": "false",
      "postConditionExecution": "ON_SUCCESS"
    }
  ]
};

sjonObj = (function filter(obj) {
    var filtered = _.pick(obj, function (v) { return v !== '' && v !== null; });
    return _.cloneDeep(filtered, function (v) { return v !== filtered && _.isPlainObject(v) ? filter(v) : undefined; });
})(sjonObj);

console.log(sjonObj);
<script src="//cdnjs.cloudflare.com/ajax/libs/lodash.js/2.4.1/lodash.js"></script>

Using some ES6 / ES2015:

If you don't like to create an extra function and remove the items 'inline'.

Object.keys(obj).forEach(k => (!obj[k] && obj[k] !== undefined) && delete obj[k]);

jsbin

Same, written as a function.

const removeEmpty = (obj) => {
  Object.keys(obj).forEach((k) => (!obj[k] && obj[k] !== undefined) && delete obj[k]);
  return obj;
};

jsbin

This function uses recursion to delete items from nested objects as well:

const removeEmpty = (obj) => {
  Object.keys(obj).forEach(k =>
    (obj[k] && typeof obj[k] === 'object') && removeEmpty(obj[k]) ||
    (!obj[k] && obj[k] !== undefined) && delete obj[k]
  );
  return obj;
};

jsbin

Same as function before but with ES7 / 2016 Object.entries:

const removeEmpty = (obj) => {
  Object.entries(obj).forEach(([key, val])  =>
    (val && typeof val === 'object') && removeEmpty(val) ||
    (val === null || val === "") && delete obj[key]
  );
  return obj;
};

Same as third example but in plain ES5:

function removeEmpty(obj) {
  Object.keys(obj).forEach(function(key) {
    (obj[key] && typeof obj[key] === 'object') && removeEmpty(obj[key]) ||
    (obj[key] === '' || obj[key] === null) && delete obj[key]
  });
  return obj;
};

jsbin


var data = [
   { "name": "bill", "age": 20 },
   { "name": "jhon", "age": 19 },
   { "name": "steve", "age": 16 },
   { "name": "larry", "age": 22 },
   null, null, null
];

//eliminate all the null values from the data
data = data.filter(function(x) { return x !== null }); 

console.log("data: " + JSON.stringify(data));