The short answer here is that you need to put all your issues in writing, and give the LL a reasonable opportunity to cure the problem. It's not your obligation to be an exterminator - he's supposed to handle that. Now, he may argue (and it's a reasonable argument) that buying mousetraps was reasonable...it's up to a court to decide.
You can attempt to withhold rent until he fixes the problems, but you need to save every penny of that rent money and it will need to be deposited with the court when he eventually tries to evict you.
But you cannot simply breach the lease and walk away.
The foregoing is not legal advice, and nothing in the foregoing shall be deemed to create an attorney client relationship. If you feel you need to speak with an attorney regarding your issue, it is recommended that you contact an attorney with expertise in your area of inquiry. The information related above is purely for informational purposes, and should not be acted upon without speaking with qualified counsel familiar with you specific situation and the laws related thereto.
The Landlord must take responsibility for any and all infestation issues. Send your Landlord a detailed letter describing the problems and demanding immediate action. If you get no response, contact the Board of Health or the local Housing inspector.
This answer is not intended to be used as actual and specific legal advice, and this answer is not intended to create an attorney-client relationship. I am happy to provide basic answers and to speak in terms of generalities, but I am not intending to give specific advice that could be construed as forming an attorney client relationship. I offer free consultations, and I am always happy to speak to potential clients personally about their legal questions. Thank you and good luck!