Given the fact that you may be the only person in history to ever want to buy Holiday Inn sheets for your home, I'm guessing they aren't for sale. There's simply no demand for the product, so Holiday Inn/IHG isn't going to go through the trouble of making them available for sale.

(I was exaggerating for the sake of comedy. You might be joined by a few dozen other people who want the sheets. But, the concept still stands.)

Given that neither Holiday Inn nor IHG have product stores on their websites, I'd say you best bet would be to ask at a Holiday Inn hotel. If possible, go to one that knows you as a repeat guest. Although I think it's unlikely, they may offer to sell you a set of unused sheets.

It's worth noting that franchise agreements between chains and individual hotels often have weird restrictions. It's been forever since I've seen a franchise agreement (and I never looked for this type of restriction), but it wouldn't surprise me if this type of sale is prohibited.

That said, I see no harm in asking a hotel.