Wash everything before you put it in there. When I was on yard I only had a limited amount of space. YOs rubbish took up the majority of the tack room. So my winter rugs came home for the summer and my summer rugs over winter. Spare tack, harness, haynets etc brought home. Rugs were washed before they went into bags when I brought them home. Initially before I collected so much stuff I used to have the rugs in my bedroom in a cupboard. But then it became unfeezable so it went into our old house at the farm. But it didn't smell as I made sure things were clean.
Depending on what size your stuff is could you get some plastic storage boxes to put things in. Alternatively I don't know if you have one near you but we have a 2nd hand red cross charity shop that is dedicated to furniture. They always have wardrobes for sale at 2nd hand prices so if you could find one with shelves might be good.
I had my nans old wardrobe down in the farmhouse which I kept my rugs in, in the bags. That's now in the tack room. When i moved off the yard I wanted a filing cabinet for my tack brushes, hat, gloves, chaps etc. The filing cabinet at the yard was the YOs but I was allowed to use it, but it worked well for small tack. So I popped in the charity shop and they had one for £25.
Alternatively have a look in your local FB page. We have a couple of freecycle ones, I know there been wardrobes and cupboards on there.
Put some smelly soaps in cupboards with the stuff.