We have an extra large cabinet where we store our extra blankets in. We fold them in the most compact way possible which really helps!
You can also just drill some hooks into the wall and hang them from there in a space that isnt being used
I really like the idea of cleaning and vacuum packing them. We have a miniature loft running over the rest of the tack, with a ladder. The rugs get folded and put up there
I use the vacuum seal xtra large bags. I hook them up to my vacuum to suck the air out and then they’re super flat and easily stacked. I always clean them before storing though.