I haven't grown tomatoes much before and this year the two that I've got are huge. I've got them in cages and I'm staking up the branches that are heading way outside the cages but at what point do I stop staking them and just start lopping off long branches so they don't bend and hang? It's starting to look like an erector set.

Nice steps are done to stop
Nice steps are done to stop the tree from getting bigger. you can also take guide from an expert gardener as well. I am going to prepare my exam 642-901 questions to achieve excellence in the career.
Tall Tomatoes
The size of a tomato vine in large part depends on the variety. Some grow big rangy vines will others stay around four feet. I will not get into all the breeding but in short the answer to your question is to just let them flop over the side of the cages.
They will continue to hang down, flower and produce fruit. So don't really worry about the size.
Mine have reached the top of the cages also (Variety Jet Star) and are starting to fall over. The good news is that the fruit will be easier to pick.
Enjoy - it is not shaping up to be the best tomato year.
Dennis - Johnson County Extension
It is perfectly OK to allow
It is perfectly OK to allow the branches to hang over the cages. If you have the space, just allow them to grow and grow and grow.