Here's our experience with rodent proofing; a lot of the suggestions should hold:
Contact landlord as a health violation or health department ??!!
Keep food and crumbs of reach. For rats there's many kind of traps. Ants don't like citrus oil, it's available in sprays. You can use sticky traps for cockroaches. Anyway keeping things clean is important. You can also dump hot powdered cayenne pepper on the perimeter etc. It will irritate most creatures.