Something I missed while reading the original post the first time.
You said small rats? It could be possible that they're just not mature enough to breed. 5-6 week old rats are "small" in my book.
Technically rats can start breeding as young as 5 weeks, but I've found that they don't breed due to their mental immaturity at that age.
I would say 3-5 month olds would be the minimum age for a female to accept a male.
I keep a rat rack in my room. I honestly can't smell them unless it's day 6+ after cleaning day. I change bedding once a week. Type of bedding and quality of food does make a difference in the odor as well.
My friend breeds fancy mice in her bed room. She probably has 20-50 mice at a time and it smells awful.
I'm temporarily housing 2 mice and one of their litters. I can't really smell them until bedding changing day.
And if you breed ASFs, there is little to no odor with them. They're a desert species so they don't urinate a lot (the main smell with mice). And when they do, they urinate in a specific "potty corner".
Here are a few tips to keep the odor down:
Change bedding at least once a week minimum.
The key is ventilation. Still stagnant air is bad. Air flow helps A LOT when keeping breeding rodents. Maybe invest in an air purifier or a small fan.
You can also put a little baking soda into the enclosures before filling it up with bedding. And putting a few drops of vanilla extract into their water bottles help as well.