There are two theories: first that the Jutes (Eudoses in Latin, Eotenas in Greek) were from Jutland, and so, presumably, spoke (as did all Danes at the time) a dialect of Old Norse, or second that they were a loose association of pirates of various tribes from around the North Sea and western Baltic who spoke languages that were still close enough for a rough mutual intelligibility. I find the first theory more convincing. The fact that they did not get on with their neighbour Angles is confirmed by the notorious amount of mental defects among 20th century inhabitants of the few villages they settled in S.E. Hampshire, presumably the result of interbreeding forced on them by their neighbours' hostility which persisted centuries after its ethnic origin was forgotten. They also settled the Isle of Wight (to the immediate south) and Kent (in the far southeast), which supports a theory that they were vassals of the Franks and invaded Britain from Gaul. "Beowulf" mentions a tribe called the Geats, related to the Goths (who originated in Gothland in S.E. Sweden, which was either synonymous with "Jutes" or simply confused with them..
Remember that the further you go back in history, the more similar all the Germanic languages are to each other.