I would dust first with an electromagnetic duster. Some areas I would use a wood cleaner. Then vacuum and change filters. Also, be aware that it may take a second round. Good luck!

I would get a bunch of disposable...or ones you ae willing to toss...towels, wet them down and get the worst of it off. Then start with the vacuum and dust cloth.

First, get a mask! I need a hit of my inhaler just reading about it!

All great info.. Thank you all. Yeah..definitely need a MASK

Use a vacuum attachment to vacuum furniture, walls etc. That would be much easier on your lungs. Once you have the worst of it up, start with a wet washcloth, rinse frequently. I buy washcloths by the dozen from Walmart and they clean better than any sponge or wipe. Cheap enough to throw away too if they get stained.

Get a vacuume with a hepa filter on it. Start with attachments and clean from ceiling to floor by vacuuming off as much of it as you can first. Then finish cleaning with a bucket of water, a rag and a mild cleaner. You will want as much of the dust gone as you can pick up before introducing any sort of water to the process. I would use a painters mask to protect yourself from dust and dust mites in the air. Open all the windows while you do this as it will help air things out while you do all this. Then, after you do all that you can go back and shine surfaces like mirrors, windows, etc. with windex or cleaner of choice.

Vacuum first, you want 99% of the dirt and dust sucked up by a vacuum. This won't take very long, then you can wipe everything down with a bucket of water and rags. Use a cleaner that has a disinfectant. I wouldn't spend too much time cleaning because you will probably need to paint and recarpet the house anyway.