When cleaning the mice cages or bins, what are you using? If you use something that has a strong smell, the males will continuously "mark" their territory over and over again and the odor will get overpowering. But if you use a "mild" solution of a bit of vinegar with HOT water, the males can still smell their "markings" and won't be inclined to mark again. You might also try to leave a bit of shavings in when you clean. Or simply remove the shavings but don't "wash" the bin <unless it's REALLY bad>.
I don't have any problem with odor though I have hundreds of mice and rats <as well as other rodents> in one room.
Part of the problem with the odor is the males feeling the need to "mark" their territory everytime you clean.
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