I think that core strength will help you not only with hills, but with everything else as well. My track coach in high school swore by having a strong core for any event. He had even us distance guys doing 500+ situps/crunches/etc every day. I'll tell you I've never had a problem due to lack of core strength after 4 years of that.
I think it helps improve speed, posture, and efficiency (all of which are probably related to some degree). Anyway, as for the hills, the best way to get good at hills is probably to do a lot of hills in your training (at least if you have them in your area). Maybe even find the biggest, beastliest hill you can and do repeats up it. Hill running also helps improve even your non-hill running too, so it won't hurt anything. I can also vouch for what Jon said. Run "tall," lean forward a little, shorten the stride, get those knees up higher, and dig with your arms just a little more than normal. That's what works for me. I like to think of it as attacking the hill. That imagery helps me beat it mentally in a race or hard run. I dunno, that's just what works for me. With a little practice Veyo will seem like a piece of cake.
