How to best get rid of musty, damp smells from different stored items.

I am about to move to a new house. The house I've been living in isn't in the best condition. Theres been damp issues etc and I have a lot of stuff thats been stacked up for a while, or stored in a shed.

Most of it smells horrible, even if its technically in good condition. Just musty and like its been in a damp place for a while. I have been driven to the edge with it tbh. I'm looking forward to a fresh start and finally being able to use some of the stuff I've had in storage. But, I will lose my mind if I transfer the smell to a nice clean house.

How can I best clean/air out the stuff to get the smell off?

I'll wash what I can, and clean my best. But I have books, suitcases, all kinds of stuff, that won't be so easy.

My current plan is to systematically move stuff to the new place, put it in a room thats tiled, open all the windows and try to air what I can in the garden (though its been raining for weeks, so good luck with that).

I've seen odour neutralisers packs and sprays online. And will happily get them if thats the way to go.

I have also looked into Ozone machines a bit. I know they are controversial, but would running that with the stuff in a room, significantly help? I have a couple of weeks overlap, where I could do that, and have the house be unoccupied. Me and my cats could wait and have that settle before fully moving in. I just want to make sure there won't be any issues for them, just having used it in the area. If thats the best, most efficient way to go, then I am happy to do further research into it, and be safe about it.

One somewhat awkward thing to note, is that I hate the smell of vinegar. Absolutely despise it. I know its used a lot in cleaning, and there will probably be recommendations along the lines of 'just put a bowl in with the stuff'. But having everything end up smelling like that would wreck me mentally. So if theres some way we could just avoid it altogether? I'd be very grateful

I know this is a long and awkward scenario, so thanks in advance for anyone able to help.