I have a troy-bilt 17.5 hp riding lawnmower and I've noticed gas getting into the oil. What could be causing these problems?

You Have A "dirty" Fuel System. The Gas Is Getting Into Your Oil Due To Your Needle Valve Not Sealing In The Carb. To Correct This , You Need To :

Remove Carb. And Clean,
Drain Fuel Tank, Add Fresh Gas Or A Cleaner And Flush Lines,
Replace Fuel Filter,
Remove The Spark Plug(s) And Turn The Engine Over , Watch For Fuel To Shoot Out,
Consider Placing An Inline Fuel Shut Off And Using It When Not Operating The Unit.
Check Fuel Transportation And Storage Can For Cleanliness.

This Is Very Common. After You Have Done The Above Task, Start The Engine For About Two Minutes To Warm Up The Oil, Drain Oil And Remove The Filter If So Equipped. Then Replace With A Quality Sae 30 Weight Oil.