I'm interested in improving my programming skills so I can get a programming job. I majored in a STEM subject as an undergrad (not CS) and used C++ for a research project. I'll have to look thru my harddrive to see if I still have the code for that, as I worked on it a few years ago. I have also worked on a few projects on my own. One of them is a simulation of a children's card game (like pokemon) and is 2000 lines of code. I've also completed a very simple poker game that takes 200 lines of code. However, the codes for these projects are messy and need to be cleaned up. The card game also functions, but I need to add more components to it to more realistically simulate the actual game

Would these be sufficient to load onto Github and increase my chances of getting a job now? Or, if my code looks sloppy enough, will it hurt my chances of getting a job?

Github (and related services) are a great way to maintain a portfolio.

I don't think that you should necessarily wait until you have a 'finished' product before you place it on github. If you are interested in showing-off for potential employers they will be just as (if not more) interested in the development process as well as the finished product.

How often does the industry sector in your part of the world ask people about their public code repositories? The last time I was looking for work (about seven monthes ago), only one of my six leads asked about it and when I told them I didn't have one, they didn't seem to care at all.

For three of them the real gatekeeper was the pre-interview coding test, and three of them didn't even have that.