Principle of Linear Superposition
not know what to do with the capacitor and the inductor in parallel


Either write the differential equations with two storage elements, or solve it as a phasor circuit with two impedances in parallel and convert back to time domain.


  how does differing angular frequencies change the summation of the two sources?


It doesn't. A + B is still A + B. Since \$\sin(\omega_1 t)\$ and \$\sin(\omega_2 t)\$ are orthogonal functions when \$\omega_1\ne\omega_2\$, there's no way to simplify \$\sin(\omega_1 t) + \sin(\omega_2 t)\$; it's already the simplest form you'll be able to write.


  due to the current division theorem, the voltage across the capacitor is also the same voltage across the inductor?


It has nothing to do with the current division theorem. It's simply the consequence of being connected in parallel and Kirchoff's voltage law. No matter what path you take from node X to node Y, you must get the same potential difference between X and Y. 


  Do the same for the current source and add the two? 


For a basic rundown of how to solve circuits by superposition, see here.