Ballistol has a pretty strong smell but some find it pleasant. I do not.
Cleaners
Hoppes Elite Cleaner (standard, not foaming) and MPro-7 are good cleaning products with little or no odor. Gunslick, Outers and Break Free all make good foaming bore cleaners that work well and have very low odor.
Don't bother with the Hoppes Elite foaming bore cleaner--I don't know why, but it doesn't work well for me. Strange since I have had excellent luck with the standard Hoppes Elite Cleaner.
Remington Bore Cleaner (NOT REMOIL) is a good choice for removing stubborn deposits from bores. It has an odor but I wouldn't classify it as a strong or particularly offensive odor. Be sure to follow the instructions--if you don't shake it well and keep shaking it while you're using it, it won't work well. It uses a very mild abrasive that needs to be shaken into suspension so that you get a good dose of it on the cleaning patch.
Most of the good nitro solvents have pretty strong odors, but if you want something that is petroleum based and will still not stink up the place too badly, you might look at making a mix of something like GooGone and ATF. I'd mix it 50/50 or maybe shade the mix towards the GooGone side to keep it fairly thin. It probably won't perform as well as a typical nitro-solvent, but it should be decent.
I typically use a nitro solvent with a bore brush and then patch out the bore. Next I either use foaming bore cleaner or Hoppes Elite/MPro 7 and leave the bore wet for 10-15 minutes. Then I patch it out again and repeat the first step until I'm happy with the results. If I can't seem to get the bore clean after a few steps, I'll use the Remington Bore Cleaner, then a nitro solvent to get all the remaining grit out of the bore.
I try not to use the foaming bore cleaners or Hoppes Elite/MPro7 with a bore brush because those cleaners tend to have some adverse effect on brass/bronze/copper materials. So I use those cleaners with patches and use the nitro solvent with my bore brushes.
Lubrication
Lubrikit sells some gun lubrication products that are not only low odor but also food safe. They are made for use on food processing machinery and, by all accounts are a good choice for firearms since they provide good lubrication properties and excellent corrosion protection.
Dillon Precision sells a product they call Snake Oil. It has no odor that I can detect and is an excellent lubricant. I don't know anything about its corrosion preventive capabilities.