Absolutely agree with above comment about Kilz or BIN. If you have carpet you should also pull that up and replace all.

Assuming it's some kind of forced air heat/AC have the ducts cleaned.

Are you in an area where hurricanes caused extensive damage? Several years back, hurricanes did so much damage in one year, the supply of sheet rock was severely diminished, and sheet rock from China ordered to fill the void. Problem was that sheet rock had formaldehyde in it, and there were all kinds of problems, the least of which was the horrific odor. Major problems included damaged plumbing(metal) and electrical wiring damage.

I'd try two things, even after all you have done. Spray Nature's Miracle on all the flooring to include the concrete. Spray along the walls where they meet the floors. That should help, if the smell is organic(not formaldehyde) pet /pest created. The priming with shellac based BIN will take care of many other smells/stains.

There are molds than can form in the walls, on the outside of the insulation. Odors from those can be intense.

There are garage cleaners that help with oil/etc. stains/smells.

If you decide to try replacing sheetrock, start with the laundry/bonus room.

I'm thinking along the lines of rrah. It may be the air that's circulating from either the laundry room or the bonus room. I have a hunch that you may have humidity in either or both of those rooms over 60%. And if so - bingo! You'll have to run a dehumidifier. Once it gets all the moisture out of the air (and the machine may have to run continuously in the beginning to do so if the humidity is indeed high) then the odor will be gone. The machine will also start to cycle on and off (instead of staying on) depending on the weather or whether you're doing laundry, which contribute to humidity levels in those rooms.

https://www.houzz.com/discussions/smoke-smell-issue-dsvw-vd~5451522?n=21

I would clean the garage floor with a concrete cleaner made to remove oil. I know Clorox makes one.. you can buy it at Walmart. There are other brands too you can buy at Home Depot /Lowe's or other hardware stores. I have used one by Behr. That may get some of the oil/musty smell out.

Thank you for the suggestion! Over the weekend, we used a strong degreaser product on the garage floor, scrubbed it, and then pressure washed it. It did take some of the oil stains out and made the garage smell a bit better overall. (And hey, any progress is good!) The odor is still pretty strong though, unfortunately, and the laundry room/bonus area still really stinks, so I’m not sure what to try next. :(

I've used hydrogen peroxide to deodorize the cement basement floor after the cat developed target issues. Maybe that could help? It is cheap to try, at least. Thoroughly dowse the floor and let it sit until it dries. If it foams, that may indicate an organic source that the H2O2 is working on.

All of these suggestions are much appreciated - we’re going to try all of these things. We have someone coming by this week to give us an estimate for duct cleaning (but I have read mixed things about duct cleaning and whether it’s really beneficial or advised to do it, so I’m a little concerned there), and we’re gonna look into inspecting inside the walls for mold. We don’t live in a high humidity area (it’s a hot, dry area that we live in) and not an area with hurricanes, so I don’t suspect a mold problem but I think it would be good to rule it out at least. We will definitely try Kilz when repainting the walls, too.

Any other ideas or suggestions though are welcome!!

OdoBan or any of the other quaternary disinfectants. (Not the original eucalyptus scent; that one stinks, IMO.)