It's mostly LabView I think, which is an interesting choice given all the hate it gets.
For those that don't know, LabView is a graphical (drag and drop) language for the most part where you interconnect various hardware components together. The advantage is that a lot of labs need to plug a lot of devices and sensors to run an experiment and LabView has support for a large amount of hardware. So you connect it all and can graphically view what the outputs are doing in chart form. The downside is that I don't think it's always very easy to specify exactly what you want to do, and code can pretty easily become spaghetti. There are a lot of horror stories about engineers having to maintain someone else's code.
Edit: -Flight software is C++ -Launch is mostly LabView and yes, they have LabView running in mission control