We clean our house regularly and shampoo the carpets often (once a month unless we spill something or a critter pees/poops then it is spot cleaned). Somedays we'll get home and the house will smell clean and "new" (how my mom puts it) while other days you walk in and you can smell the animals as soon as you walk in. The ferrets litter is cleaned daily and all the bedding is washed weekly (same with the dogs). But what else can make a house smell clean?

I hate using candles or other "fake" scents because they don't last long and just cover up the bad smell..

Also, we open our windows often to give the house an "airout".

I bought a huge box of lavender buds and made dozens of sachets. Keeps mice and bugs out of my storage bins here in the country and I hang them in closets and bathrooms. Lots of other dried plants work too, any kind of pot pourri made of flowers and cedar and spices. Bayberry. Lemon peel. Orange stuck with cloves. Geranium oil is so strong it can be used to keep dogs away from a female in heat, I've heard. Baking soda sprinkled on carpets and vacuumed. Clean with vinegar - I like the natural smell and it cleans just as well as any expensive product, or better.
You probably have more smell on humid/damp days?
Try to fence off most of the area where pets shouldn't be going, because once they do, they go back to the same spots. I use foam insulation (blue or pink and 2" thick) as gates because it's so light and can be cut to fit.