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.
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I agree with Mr. Keppler. I do not know the level of infestation, but in may be worthwhile to have the Board of Health inspect.
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!