"I got a great deal on synthetic car oil so I bought some for my bike. Now the clutch is slipping and the transmission sounds louder for some reason. What's up?"
You've likely encountered several problems while using the synthetic automotive oil. The first being that oil for motorcycles should meet the JASO-MA specification (no friction modifiers) or the JASO-MB specification (with friction modifiers) which most automotive oils do not.
Reason being, automobiles have dedicated transmission and motor oils (they're separate from each other) where most motorcycle transmissions share oil with the motor. This means motorcycle oil must be more versatile since, essentially, it needs to be two oils in one.
Back to your problem, the clutch is likely slipping because many automotive oils use friction modifiers (additives) that make the oil extra slippery to improve gas mileage-these additives aren't compatible with a clutch since they are too slick, causing it to slip. On the other hand, motorcycle specific friction modifiers are OK for your bike since they're JASO approved for both the transmission and the engine.
In regard to the extra gear noise, this again stems from the fact that automotive oils aren't suited for transmissions. The gears inside a transmission are under a unique type of stress called shear load, and this requires a special type of modifier that car oils don't have. That extra noise is the lack of shock protection in the automotive oil, which causes serious gear wear.
Make sure your motorcycle oil meets the aforementioned JASO specs or you could seriously jeopardize your ride. Remember, all oils aren't created equal and being too frugal with your selection could cost you a fortune.