So I've lost 50lbs so far and I've recently started to really notice the way I walk. My hip movement feels strangely awkward. I was just wondering if anyone else had this issue as well, and if so any idea why?

I'm going to guess that your weight loss is reworking the way your muscles support your body. As you weigh less, they have different support stress spots, and are probably realigning themselves to balance you. Same with your joints and feet. Just my theory!

I noticed when I was running recently that I swing my arms with my elbows out. Then I realized I did that because to keep my arms from bumping into the fat on my sides when I ran. I am thinner now and don't need to do that anymore. But when I tried to run normal with my arms in, it felt awkward and I couldn't do it.

Weird.

I don't have any answers for you, but it doesn't sound like what's happening to you is a bad thing.

It might be that your center of gravity is changing as you lose weight and that your body isn't immediately making the adjustment to it (kinda like how adolescents go through an "awkward," clumsy stage of bumping into everything since their body is growing faster than they're used to).

I'm sure your body will adjust over time. Love your avatar, by the way.