A 10 is too small for corydoras. They need 30 gallons minimum. Also, they are very sensitive to ammonia and nitrites and so should not be in tanks that are cycling. 10 inches of fish (mature growth, not how big it is now) is absolute maximum for a 10 gallon and that's only if the filtration is for a tank 2-3 times that size. Tetras, and any schooling fish, also need more room than a 10 can give them. Even if the cory cats were OK, they get to be 3" and would account for 9 inches of fish. Add the bettas -- at least 4" -- and the gouramis -- 3" -- and you've got at least 16" of fish. Way too many for so small a tank. It's best to get a larger tank, but remember, it's never going to be large enough for what you want, so decide on the largest you can manage and be conservative with the number of fish you put in it. Here's a good site for recommended tank size for various fish:
http://www.peteducation.com/category_summary.cfm?cls=16&cat=1911
