Generally speaking "less is more." In this case the clearest solution is "There are many activities including, but not limited, to running, jumping (,) and swimming.
The "Oxford comma" between "jumping" and the "and" is optional. If included it clearly distinguishes the three separate activities with no potential to think that "jumping and swimming" is somehow "one activity type" that includes both jumping and swimming.
However, the two different activities of jumping and swimming are distinct enough that there is little chance of confusing them as one activity. In this case the "Oxford comma" in parentheses above is also not necessary. So following the principal of "less is more" I recommend the simplest and clearest solution is "There are many activities including, but not limited, running, jumping and swimming."
Regards
Bill