You can never go wrong with genuinely asking someone how their day is going. If someone doesn't want to talk it's very easy for them to shutdown the conversation and move on. But, I find most of the time people are dying to talk about how good/bad their day is going.

Think of it this way. Everyone's favorite topic is themselves. Give someone an opportunity to talk about themselves and most people will take it. The nuance that takes practice is not peppering the person with questions. Ask, give them time to respond, and then maybe say something from your own day and ask a follow up to something they said. That way you keep them doing most of the talking, but it's not an interrogation.

As for the awkward part, embrace it! I can be super awkward so I just run towards it. "Ending a random convo is always awkward for me, so I'll just say it was nice to chat and maybe chat again sometime." Usually there's a chuckle and done.