Hi there, if you have signed a lease, but even if its just an ongoing tenancy after 3.5 years, the landlord is responsible for ensuring the house is safe and habitable. Mice poo in your house and especially in the oven is not safe, and if you were to have a community health worker come out to your home I'm sure they would back you up. You could and have probably tried baits etc yourself but obviously if they are everywhere then THE PROPERTY (not you and your family) has an infesation. I would be giving 14 days written notice for the landlord/agent to organise pest control or after which time that has not occured, you will be organising pest control of the property and yourself billing it to them. I'm in NSW, I wouldnt be putting up with it. Might be diffrent where you are in regards to the number of days you have lived there etc.
Sounds like the landlord/agent is just being plain lazy, it really gets my goat up lol