Climbing up Strawberry Peak from the west just plain sucks. From the top of Colby Cyn Trail to Strawberry Peak the trail is basically unidentifiable over the first hill or two. Once you clear that, you'll be bouldering straight up the mountain, so be prepared. Don't take your dog on this route...they won't be able to climb up.
I would not want to try coming back down the western route, it's way to steep. Might as well make a day of it, continue down the eastern side, then enjoy the much gentler trail around Strawberry Meadow.