looks like the kings play calgary on monday april 6th and the oilers on the 7th... i'd recommend flying into calgary for the weekend. maybe get out to the mountains for some spring skiing/boarding or sightseeing in banff for a day. i'd recommend a hotel downtown or just outside (ie hotel arts) so that you're close to the dome, restaurants, night life, etc. depends on your budget though.
as for the game in edmonton, i'd look into either renting a car or hopping on the greyhound on the tuesday. depending on what you wanna do, you might look into flying back to LA from Edmonton.
http://www.westjet.com has a seat sale going on right now. direct flights from calgary to LA (maybe edmonton too?)
oh and definitely line up your tickets ahead of time if you can. these games will likely be sell outs as usual, so ebay or some other re-seller is your best bet.
weather is pretty unpredictable at that time of year. anywhere from a spring snow (below freezing) to 50-60's F (which is still cold for LA, i guess)