A321 pilot reported a bird strike on departure caused a fumes event and a return to the airport for an overweight landing.

Narrative

On climbout of ZZZ smelled a food burning smell. I thought Flight Attendant (FA) was cooking our crew meals. Got a call from FA later during climb that smell was strong throughout cabin. First Officer (FO) then said he saw a bird go by on climbout that he thought we may have hit. After discussing issue with Operations and Maintenance control via crew phone; I decided to return to ZZZ and land overweight per their suggestion and the fact that we had the fume event happening. [Priority handling was requested] for overweight landing and bird strike on takeoff. Airport Rescue and Firefighting (ARFF) was called out and they followed us to gate inspecting the engine for damage and to ensure no fire ignited. Passengers were deplaned. Got a new plane and departed for ZZZ1 again 4 hours late. Bird strike was in number #1 engine as evidenced by blood and feather debris noted by us and maintenance on post flight walk around. This was written up in Aircraft Maintenance Logbook (AML). Overweight landing was written up in AML with required parameters also. Another AML write up was done for item not related to this event as well.No suggestions.