What a terrible situation to be in! So the landlord is saying "If they aren't born here, they aren't our problem!" That is amazing. This is a tricky one. You are not creating the unsanitary situation and you can show that it is coming from the unit across the way. The landlord's failure to help you with this issue is interfering with your ability to enjoy your unit. Additionally, the landlord must "make all repairs and do whatever is reasonably necessary to put and keep the premises in a fit and habitable condition." I would recommend putting more pressure on the management to fix this situation. At the very least, they should get the adjoining unit to clean up their act. If that fails, you should probably talk to an attorney, especially if the problem is unbearable. As a caution, do not simply stop paying rent without talking to an attorney. Ohio has very specific rules on how to "withhold" rental payments. Good luck!
Mr. Andersen's answers are not intended to create an attorney-client relationship and are based on only the limited information provided in the question. Thus, they should not be considered as legal advice, and persons seeking legal advice should contact Mr. Andersen directly and/or another attorney with a law license in the state in which your situation arose. Mr. Andersen is licensed to practice law in Ohio.