That chocolate and strawberry cake sounds like a good idea (i've done it before with devils food and red velvet). Using white cake with jello won't work, since it will change the consistency of the cake. If you want to go with a really strong flavor though, use a box of strawberry cake mix and add a can (12 oz, or 1 and 1/2 cup) of strawberry soda. This sounds odd, but it does work, and I do this very often (my husband prefers soda cakes to normal cakes -_-), though using a fruit soda may make it too sweet (I always use sprite or diet rite, though sometimes i'll use Dr. Pepper).
As for the Frosting, I second the cream cheese idea. How I make mine is one 8oz pack of cream cheese, one small tub of cool whip, a teaspoon of vanilla and about 1/3 to 1/2 cup of sugar. Mix it all together until it's mixed (it will be a little runny), then turn up your beater and whip it until it's stiff and fluffy. When you refrigerate the frosting, it'll firm up a lot, and tastes like a really light cheesecake.