Are sonatas a good platform for turbos?
 

I was wondering how strong the Sonata engines are and do they hold up to turbocharging well? What about supercharging?

I see you have the 2.7l? That's the same as the V6 in the GK Tiburon.

The engine responds well to turbo or supercharging. I would limit yourself to around 300lb/ft supercharged or 350lb/ft turbocharged if you don't want to build the engine but if you treat it fairly nice you should do fine at those power levels. If you could upgrade one other thing, it would be getting a custom torque converter. That'll be the first thing to go if you abuse the car.

Is it true that the 3.3 V6 can't handle a turbo?

Any engine can handle forced induction as long as you take the proper steps in building things correctly.