In every state landlords have responsibilities to maintain the property habitable. Mice infestation is one of the things considered affecting habitability of the property. You might want to check your state habitability board to find out whether mice are on their list. The phone number is (609)633-6241. If the landlord broke the implied warranty of habitability, then you would have a number of options including rent strike, repair and reimbursement, constructive eviction, etc.
Your problem, however, is that now the landlord is claiming you caused the problem by not keeping food in closed containers. Whether that is true is up to debate. If you did cause the problem, then the landlord is off the hook of IWH and probably will go after you for damages.
One thing is problematic for you, as you told, you moved into the property four months ago and only found this mice problem about a month earlier. The old traps might be just too circumstantial to prove anything. Here is what you need to do. One, fix the problem as directed by the landlord. This is for your benefit as well. Two, gather evidence, from other tenants if you will, and from the extermination companies, to find out whether this problem occurred before you moved in such that you can hold the landlord liable for breaking the warranty.
