Such systems are easy if you breakdown the problem into different parts.
Firstly, you need to keep track of everyone's combo kills using an integer array where the index maps to the player's hero.
Every time they kill a hero, add 1 (incriment) their combo kill counter by 1. Everytime they die, reset their combo kill counter to 0.
When they kill a hero and their counter is greater than 1, you award them combo gold based on the number size (as well as display easilly generated text and sound).
Obviously team kills should not incriment the combo counter for the player but should reset the TKed player's combos.
For double and tripple kill, you use a timer and an integer (multi kill) array with index for each player and start it when they kill an enemy hero (timeout of 5 seconds is about right). If the timer timesout, they will not be able to receive a multi kill so the multi kill is set to 0. If they make a kill and the multi kill is not 0, then they have made a multi kill and you award bonus gold (as well as sound / text) based on the number it reaches (resetting the timer each time).
Thats all there really is to it...