How can I merge multiple tabs in a Google Spreadsheet using Google App Script?

You don't need a script for this. In the fourth sheet, enter the following formula in A2:

={filter(Sheet1!A2:C, len(Sheet1!A2:A)); filter(Sheet2!A2:C, len(Sheet2!A2:A)); filter(Sheet3!A2:C, len(Sheet3!A2:A))}

It returns the contents of columns A-C where the entry in column A is nonempty, and stacks them in one array.

=query({Sheet1!A1:C; Sheet2!A1:C; Sheet3!A1:C}, "where Col1 is not null", 0)

I wouldn't use a script for this; the worksheet formulas are much faster, at least most of the time. Make sure you use semicolons to separate the ranges. Semicolons are the End_Of_Row operator for array literals.

If you really want to use a script...

function combineSheets() {
  var sApp = SpreadsheetApp.getActiveSpreadsheet();
  var s1= sApp.getSheetByName("Sheet1");
  var s2= sApp.getSheetByName("Sheet2");
  var s3= sApp.getSheetByName("Sheet3");
  var s4= sApp.getSheetByName("Sheet4");
  //  If Sheet4 doesn't exist you'll need to create it here.
  
  var s1values = s1.getRange(1,1,s1.getLastRow(),3).getValues();
  var s2values = s2.getRange(1,1,s2.getLastRow(),3).getValues();
  var s3values = s3.getRange(1,1,s3.getLastRow(),3).getValues();
  
  //  Now, we can put out all together and stuff it in Sheet4
  var s4values = [];
  s4values =  s1values.concat(s2values,s3values);
  s4.getRange(1,1,s4values.length,3).setValues(s4values);
}

You can use Google Apps Scripts for this.

var ss = SpreadsheetApp.getActiveSpreadsheet();
function TotalsSheet() {
  var totaldata = [];
  var sheets = ss.getSheets();
  var totalSheets = 2;

  for (var i=0; i < totalSheets; i++) {
    var sheet = sheets[i];
    var range = sheet.getDataRange();
    var values = range.getValues();

    for (var row in values) {
      totaldata.push(values[row]);
    }
  }
  return totaldata; 
}

function Start() {
  var All = ss.insertSheet("All-Values");
  var totaldata = TotalsSheet();
  for (var i = 0; i < totaldata.length; i++) {
    All.appendRow(totaldata[i]);
  } 
}