what are the widest 700c available(with kevlar)? Is it possible to put wider tires on the wheels I have? 
(original wheels on a Giant hybrid...GX-02 622 x 19)

I have 700c x 38mm(Schwinn kevlar tires now). I would like something similar...TIA
Yes, it is generally possible to install wider tires that those which came with a bike.

The limiting factors are the clearance available in the forks and frame. The chainstays/bottom bracket area is usually the most constricted area.

The rims will also have a maximum size of tire they can support, but the frame clearance is likely a more limiting factor.

If you have 38mm tires now, you can probably step up to 40 or 42mm.