What kind of litter are you using? Wood shavings don't absorb liquid or odor very well. Try a wood pellet, recycled paper or similar type litter. They break apart when wet are are safe for rabbit. Do not get clumping cat litter as it can cause blockages if eaten and is also dusty which can lead to respiratory issues.
There are some pet cleaners that get rid of the enzymes in the urine. I am not sure if they are safe for birds, but it could be something to look into. They are more for use in fabrics like carpet, but could probably be used for the cage too.
Cleaning the cage bottom really well is a good idea. I clean using hot, soapy water and white vinegar if there are harder to clean spots.
You might need to clean his scent glands. They are on both sides of the gentiles. A Q-tip will work. They can smell really bad, so be prepared for that