I recently compared some motors I could find online. A 20hp 2 or 4 stroke motor may weight under 50lbs whereas a 20hp electric motor may weigh 300lbs! What are the determinants of electric motor weight and power? What are prospective avenues for reducing the weight of electric motors while increasing their power?

There is research ongoing. I found the Dyson motor, don't know what it worths.

Motors need magnets and conductors. Conductors are generally metal. If you trade conductivity for weight you lose efficiency or increase cost. e.g. copper is about twice as conductive as aluminum.

On the Wikipedia there is an article http://en.wikipedia.org/wiki/Power-to-weight_ratio

Acording to this article , there are electric motors that are comparable to IC (some of them used in hybrid vehicles). It seems that an ordinary motor has low power-to-weight ratio because 'nobody' cares about its weight (price is more important). Obviously, there is a room for power-to-weight ratio improvement if you are ready to sacrifise price or reliability.

 

Still, as Swansont partially said, electric motors need strong magnetic flux, and so (without using superconductivity) must contain bulk of ferromagnetic material - iron. Unfortunately, iron is heavy and electric motors cannot easily compete to IC engines.