Would it be bad for health to store a two stroke motorized scooter in a small room with me? Or would it stink like fuel etc?

There are always solutions. 

Run the engine out side until the engine, gas tank, and carb are empty.

Search Amazon, or JP cycles, or just Google motorcycle covers. Some companies make and sell a big, zippered, plastic bag that completely encloses your bike. It's like a big sandwich bag.

Well, it would stink but what you need to watch out for is striking a match with all those gasoline fumes around.  All it takes is the right mixture of gasoline and oxygen and BOOOOOOMMMMM!  Funeral sometime in the next few days!

It will smell like 2 stroke oil.  Once the muffler is cool enough to touch with the hand you could put it in a plastic bag like a bread bag while you store it inside and that won't stink as much if at all.  Then take the bag off when you are ready to ride.

Some can tolerate the smell of gas, and motor odors.  

A great many more can not tolerate even the thought of it. 

Yes it would stink like gas

Lock it up outside. 

Everything in the room will start smelling like the bike. Gas fumes indoors are unhealthy. The fuel tank cap should seal some, but the carburetors will give off fumes. 

It would smell, no doubt about it. And everything else in the room would smell eventually.

I doubt it, but you could always get a heavy cover and put in on there.

Yes.  Get it out of there.