My daughter had the same sort of problem, but her vents are in the ceilings, so we knew the kids or cats could not have put anything ‘down’ them! She did think that a squirrel or some sort of critter may have come in thru the attic and died in a vent. It got bad enough they called the A/C company out but he didn’t find anything. He finally determined that it was the smell that comes from it not being used since last summer. We were not quite sure, but it finally dissipated after about another week. Her unit is in the attic and hard to clean without making a mess. My old house had the unit where I could get to it, and I sprayed the coils with bleach/water solution every spring, and flushed it through the lines. It still had a slight musty odor the very first time, but otherwise it did quite well.
Good luck with it, anyway!