I look weird from the side too. But if you think about it...when we look in a mirror or whatever we see the front of our faces. We see ourselves from the side view a lot less frequently, so we aren't really accustomed to it. That's probably a big part of the reason why it's 'weird'..
I definitely think that different angles can make you look better or worse. I see that every time I take pictures of myself. LIghting tends to make a difference, too. But to answer your question simply... yes, some angles make you look better than others.