"How much should I talk about my strengths? Is it better to talk a lot about them or would that look like I'm bragging?"
I think that when you're interviewing, your resume really should be listing all your strengths. So people will put their academic qualifications on their resume. They'll put their firm experience on their resume. They may put other things on their resume. You can bring up your strengths, but a lot of times you need to be careful and you don't want to turn people off. And it's especially true if you're an associate and you're talking to another associate, you want to be careful about that.
Your resume really should talk about your strengths, the biggest strength you can talk about when you're interviewing and the best way to show your enthusiasm is to talk about your enthusiasm for the work. Talk about how much you like being an attorney. Talk about the fact that the more you do it, the more you like it. Talk about your, maybe you have a philosophy about trying to do the best thing for your clients possible or save them money, whatever it is, those are important things that should be brought up. Those should be your strengths. General strengths that anybody can possess are better to talk about than saying, you're the smartest person in the room, or you got the best grades, or you're a great orator or all those sorts of things that can help the firm, but aren't necessarily going to be alienating.