encodeToBig5.js

var iconv = require('iconv-lite');
var buf = iconv.encode('測試', 'big5');  // <buffer B4 FA B8 D5>

var bufLength = buf.length;
var test = '';
for (var i = 0; i < bufLength; i++)
  test += '%' + buf[i].toString('16').toUpperCase();
  
// test = %B4%FA%B8%D5

gistfile1.js

var smsData = {
    username: 'username',
    password: 'password',
    smbody: encodeToBig5('測試'),
    dstaddr: 'dstaddr'
  };
  
// Create query

var query = unescape(querystring.stringify(smsData));
//  auerystring.stringify => 'username=username&password=password&smbody=%25B4%25FA%25B8%25D5&dstaddr=dstaddr'
// auerystring.stringify will encode '%' to '%25'
// use unescape to turn '%25' back
// unescape => 'username=username&password=password&smbody=%B4%FA%B8%D5&dstaddr=dstaddr'