Heard a bunch of people claiming that there was a study that EpiPens were found to be medically effective well past their expiration date.
Is the claim true, and if so how sound is the study?
Yes, there was such a study, if by "medically effective", you mean something like "better than not using any epinephrine treatment".
From the NIH, a study first published in the Journal of Allergy and Clinical Immunology titled "Outdated EpiPen and EpiPen Jr autoinjectors: past their prime?":
For prehospital treatment of anaphylaxis, we recommend the use of EpiPen and EpiPen Jr autoinjectors that are not outdated. If, however, the only autoinjector available is an outdated one, it could be used as long as no discoloration or precipitates are apparent because the potential benefit of using it is greater than the potential risk of a suboptimal epinephrine dose or of no epinephrine treatment at all.
The linked abstract is pretty clear: the effectiveness does decline, and some units will be discolored or contain particulates, but the data appear to support a conclusion that if you have no other choice, an expired treatment is better than none.