Could they be filled with junk?
Routers are not drives (HDD or SSD) and do not store data as such, so no, they do not collect "junk" in the operating system sense of the term.
Might then need "flashed"?
Flashing the firmware on the old router might be a good idea, but make sure it is available and IF there are any upgrades. Also...will the firmware upgrade benefit you? Same principle as flashing your BIOS on your computer. Yes, you can do it, but will it make the computer run better? Not necessarily. Depends on what is being offered on the upgrade and what your need is. Do your studying first.
software I could get to test them out?
Not to the best of my knowledge. You have to run them and if you have problems, then you troubleshoot from there. Another thing: if these are old routers, you may be doing yourself a disservice in performance and especially security of your system. One thing you will have to decide is if the problems you are having (that you mentioned in your post) are from an infected router with a virus, or that it is just old and not handling the speed and data streams well. Some of these new routers used by gamers are running 5GHz, which does not mean necessarily that they are faster than a 2.4GHz router, but definitely a cleaner signal and other advantages which will help your online gaming.