Using global variables in Jenkins Pipeline

Try following and see how it goes:

def ZIP_NODE
def CODE_VERSION
pipeline{
    /*A declarative pipeline*/

    agent {
        /*Agent section*/ 
        // where would you like to run the code 
        label 'master' 
        }
    options{
        timestamps()
        }
    parameters {
        choice(choices: ['dev'], description: 'Name of the environment', name: 'ENV')
        choice(choices: ['us-east-1', 'us-west-1','us-west-2','us-east-2','ap-south-1'], description: 'What AWS region?', name: 'AWS_DEFAULT_REGION')
        string(defaultValue: "", description: '', name: 'APP_VERSION')

        }
    stages{
        /*stages section*/
        stage('Initialize the variables') {
            // Each stage is made up of steps
            steps{
                script{
                    CODE_VERSION="${BUILD_NUMBER}-${ENV}"
                    ZIP_NODE="abcdefgh-0.0.${CODE_VERSION}.zip"
                }
            }                
        }
        stage ('code - Checkout') {
            steps{
                println "checkout skipped"
                //checkout([$class: 'GitSCM', branches: [[name: '*/master']], doGenerateSubmoduleConfigurations: false, extensions: [], submoduleCfg: [], userRemoteConfigs: [[credentialsId: 'xxxxxxxxxxxxxxxxxxxxxxxxxx', url: 'http://xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.git']]]) 
            }  
        }

        stage ('code - Build'){
            steps{
                sh "echo ${JOB_NAME} && pwd && echo ${ZIP_NODE} && echo 'remove alraedy existing zip files' && rm -rf *.zip && zip -r ${ZIP_NODE} . && chmod 777 $ZIP_NODE"
            }
        }
        stage('Deploy on Beanstalk'){
            steps{
                println "build job skipped"
                //build job: 'abcdefgh-PHASER' , parameters: [[$class: 'StringParameterValue', name: 'vpc', value: ENV], [$class: 'StringParameterValue', name: 'ZIP_NODE', value: ZIP_NODE], [$class: 'StringParameterValue', name: 'CODE_VERSION', value: CODE_VERSION], [$class: 'StringParameterValue', name: 'APP_VERSION', value: BUILD_NUMBER], [$class: 'StringParameterValue', name: 'AWS_DEFAULT_REGION', value: AWS_DEFAULT_REGION], [$class: 'StringParameterValue', name: 'ParentJobName', value: JOB_NAME]]
            }
        }
    } 
}

I got following output:

Started by user jenkins
Running in Durability level: MAX_SURVIVABILITY
[Pipeline] node
Running on Jenkins in /Users/Shared/Jenkins/Home/workspace/test
[Pipeline] {
[Pipeline] timestamps
[Pipeline] {
[Pipeline] stage
[Pipeline] { (Initialize the variables)
[Pipeline] script
[Pipeline] {
[Pipeline] }
[Pipeline] // script
[Pipeline] }
[Pipeline] // stage
[Pipeline] stage
[Pipeline] { (code - Checkout)
[Pipeline] echo
21:19:06 checkout skipped
[Pipeline] }
[Pipeline] // stage
[Pipeline] stage
[Pipeline] { (code - Build)
[Pipeline] sh
21:19:06 [test] Running shell script
21:19:06 + echo test
21:19:06 test
21:19:06 + pwd
21:19:06 /Users/Shared/Jenkins/Home/workspace/test
21:19:06 + echo abcdefgh-0.0.17-dev.zip
21:19:06 abcdefgh-0.0.17-dev.zip
21:19:06 + echo 'remove alraedy existing zip files'
21:19:06 remove alraedy existing zip files
21:19:06 + rm -rf '*.zip'
21:19:06 + zip -r abcdefgh-0.0.17-dev.zip .
21:19:06 
21:19:06 zip error: Nothing to do! (try: zip -r abcdefgh-0.0.17-dev.zip . -i .)
[Pipeline] }
[Pipeline] // stage

sh '''
'''

should be

sh """
"""

with single quotes the variables don't get processed.