There are many problems with your request.
1. Well, just starting with the memory, you've narrowed it down to Fuji and Olympus as the only ones that take xd and sd in the same cameras, since you require both.
2. There are cameras that can do ISO 1600, but noise degrades the photos so much that it's not very useable. I have the Fuji F20, and it can't even do 1600 that doesn't leave a ton of noise.
3. There are no superzooms under $200. Closest is around $250-$280
4. It's not physically possible to make an ultracompact superzoom(5x is the largest focal range in ultracompacts I know of).
If there was a superzoom that could pull off good photos in ISO 1600, somewhat compact, and priced $700 then there wouldn't be as many DSLRs sold.
This is the closest I found to your requirements:
http://www.amazon.com/gp/product/B000NOUP0S/sr=1-5/qid=1213599210/ref=dp_cp_ob_title_1?ie=UTF8&qid=1213599210&sr=1-5
It's not ultracompact and could easily be argued as being compact. It's 7.1MP, not the 8-10 you wanted, but I'd still take a 6MP Nikon D40 photo printed out to 11x14 over any point and shoot.
You can see how much noise is prevalent in each ISO setting on this review.
http://www.dcresource.com/reviews/fuji/finepix_s700-review/
Pretty much all the point and shoots will perform about the same in high ISOs.
Well, I'm on the hunt for the perfect digital camera for me, but just cant find a good one. So, I came here for help. This is going to be challenging...
Megapixels: 8-10
Optical Zoom: 8-10
ISO: Must be 1600
Digital Camera Type: Ultracompact
Price Range (The Challenging part): Under $200
Preferrebly if the camera took both SD/SDHC and xD memory cards.
If anyone can find the perfect camera. It would be a great help.

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