Science time!
Plyometric exercises increase your running efficiency, thus making you faster. Same goes for strength training.
Source:
https://www.researchgate.net/profile/Mikel_Izquierdo/publication/248384281_Effects_of_Plyometric_Training_on_Endurance_and_Explosive_Strength_Performance_in_Competitive_Middle-_and_Long-Distance_Runners/links/02e7e52c70e39c3f37000000.pdf?origin=publication_detail
Cycling is roughly equivalent for VO2 Max, compared to running for the same amount of time. But cycling isn't going to improve running economy nearly as much. Therefore, if two athletes train for the same amount of time but one cycles and one runs, they'll have the same relative VO2 max but the runner will be faster at running. I believe this is usually understood to refer to stationary bikes, since riding a bike for 45 minutes downhill and riding a bike for 45 minutes uphill are very different lol.
Source:
https://libres.uncg.edu/ir/asu/f/Honea,%20David_2012_Thesis.pdf
I think the elliptical was slightly less effective than cycling but I don't know if it was significantly so.
So, unsurprisingly, cardio workouts are good for VO2 max but strength type workouts are better for economy (explosive type strength, not sure about endurance type strength). You might think that VO2 max is more useful, but for many running it may be more beneficial to improve running economy. There are many recorded cases of athletes getting significantly faster despite a slight decrease in VO2. In the studies looking at explosive strength, the subjects doing the explosive training normally perform better than the control group, but their VO2 max decreases while the control group's either stays the same or increases.
There was a study that showed bike sprints (very hard effort with short recovery) to be effective for improving times, if you want to combine the two. I'll post the link to the study when I find it.
In one of the studies of explosive pyrometric training, the control group spent very little time doing pyrometric training but significantly more time doing circuit training (core and leg exercises). They did not improve their times significantly. I would agree that this type of training is better for injury prevention than actually getting faster. I don't think this type of training is useless but I'm not sure what it's most effective for.
I don't have any science for soccer, but whenever we have a soccer player try out for track they're normally varsity level or close to it. So anecdotally, soccer is great for running.