Node.js Cannot read property 'on' of undefined

You forgot to return the event emitter from your v function:

var v = function() {
    var e = new events();
    e.emit('start');
    return e;
};

Also notice that the start event will not be called because you have emitted the event before you subscribed to it. So you could kind of rework your code a little:

var events = require('events').EventEmitter;
var v = function() {
    var e = new events();
    return e;
};

var r = v();
r.on('start', function(){
    console.log('event start just fired!!!!!!!!!!');
});

// emit the event after you have subscribed to the start callback
r.emit('start');