Just looked on IMLeagues, I think your best option would be to create a new league for each event all under the same sport. There seems to be an option for heat scheduling which I think would be valuable for track and field events. The other option would be to have the one league and each game would be a different event. I would think this would work well for an event where each team or individual has to compete in every event.
We are a school with about 2,000 undergrad students. We have tried single day video game tournaments but the turnout tends to be low. I would say on average we would get 5-10 participants but would often have no shows. I'm sure we all know how troublesome no shows can be when you are planning a tournament. I think over the last several years the video game environment has really changed. I have had many students tell me they would rather play with their friends online. If you already have the systems, it's worth trying but to invest in all the equipment you will need to run one tournament I would say is not worth the hassle. One thing I would say though, if you have a group of students really interested in running this tournament, I would encourage them to help organize it. If you have a group of students really excited about it they may be able to get more students to join in.