Viriya and virile are. Viriya comes from vīra ‘mighty one, hero’, virile comes from vir ‘man’, both words having very similar phonetic appearance and meaning roughly the same things; in fact, vir is even mentioned as one of the cognates for vīra. Cf. also the archaic English weregild ‘man’s price’ and English werewolf ‘man wolf’. The hypothetical Proto-Indo-European word form is wiHrós, derived from *weyh₁- ‘to hunt’. so the earliest reconstructed meaning of the word is ‘hunter’: a pretty far cry from *weg- in the Proto-Indo-European language. Since the words look kind of similar and one may argue that their semantics can ultimately be shown as related, before looking into the rules of phonological changes in Indo-European roots it is not ruled out they could have been related in a still earlier language stratum. However, the current state of the historical linguistics does not really allow to reconstruct this stage with any certainty, e.g. the hypothetical reconstruction of Proto-Nostratic roots has been subject to substantial criticism in the past decades. So, it is safer to say vigour is not related to viriya and virile.
tl;dr: viriya and virile are related, viriya-virile and vigour are most likely not.
P.S.: a dicitionary giving the infinitive as the base form for Latin verbs is so-o-o-o-o not posh 