Having had to do this for my dad most of this year I’ve got a few tips:
Get a big plastic container to use as a makeshift sink and something to scrape with too. Deal with it quickly before it dries. A small board can be handy for using as a flat surface to work on the soiled clothes.
Use doggy door bags to help pick the bad ones off, pick lump off then spin the bag inside out and tie. They are literally designed for this and some even help mask the smell too. Check with the council how to dispose of them (I was ok to put them in general waste black bags).
Wash the container out after every use, a quick spray with some bin deodoriser keeps things in check.
Use a proper anti-smell detergent when you wash the clothes. Nothing I’ve found can touch Halo Sports Wash but it is hard to find currently, I found this HG additive is nearly as good but gets expensive when you add the cost of regular detergent on top.
When clothes get to the point that cleaning won’t get rid of the smell or stains, even slightly, just get rid of them. Las resort can be one of the various Vanish sprays but they tend to eat the fabric if you need to sue a lot of it.
If you possibly can have a washing machine set aside for doing just this dirty stuff it at least do a few washes in a row, it can sometimes take an empty cycle with cleaner to remove the smells, otherwise that can transfer to the next load of washing. Also keep on top of filter cleaning too.
Have a set of your own clothes you can change in to quickly that you don’t mind ruining, splashbacks are a hazard!
Most of all try not to get disheartened about doing it. They (presuming your parents) cleaned you up when a baby so it’s only fair you return the favour! You do eventually become desensitized to it, ask any nurse.