What action can I take? I want to teach this person a lesson for the absolute unprofessionalism he has shown. Not serving notice + not paying + no handover / documentation of work (this has cost us most).
You have to refer to the employment offer letter for the clauses binding on the employee while he accepted the employment offer.
If he is required to pay the notice period or serve the same, you may inform him about this in your legal notice to him.
In the same notice you may instruct him to handover the company's property or else to face legal action both under civil and criminal laws on this.
You may even declare him as absconder as his resignation without following proper procedures is not in accordance with law and hence rejected.
You can engage the services of an advocate to issue a proper and strongly worded legal notice first and then initiate action as per provisions of law.