Nennius is interesting for the genealogies he gives, but doesn't take Woden's line back beyond Geat, called him son of a god. He makes no effort to link Wodan with a god or Troy as in Sturluson's stories, although he does trace the Britons back to Brutus of Italy, then via Aeneas on into Biblical material (but gives various lines, one from Japheth and one from Ham).
He does however say that the Saxons descend from Saxo, son of Negue, son of Alanus, the first man in Europe. Alanus is son of Fetiber, and then the line is traced back through names also found in Irish national genealogy, back to Javan, son of Japheth. He then says the British descend from Britto, son of Hessitio, another son of Alanus, but calls Alanus the son of Rhea Silvia (and hence the wife of Fetiber?), daughter of Numa Pompilius, son of Ascanius, son of Aeneas of Troy. Nennius makes no mention of where the Angles or Jutes came from.
It is certainly interesting to see the different family lines, showing the lack of concensus, and some clues as to how the genealogies developed.
Asser takes Wodan's line back to Geat (called a pagan god), then back through a much shorter genealogy than in Sturluson, back to Sturluson's Sescef (missing out completely any link to Troy), whom Asser seems to equate with Seth the son of Noah (the Anglo-Saxon Chronicle says this Sescef/Sceaf was born in the ark). Asser equates the Goths with the Jutes, and makes them related to the Saxons.
Sceaf also appears in Beowulf, and in William of Malmesbury, as a mysterious child found in a boat that drifted in from the sea.
It looks like the linking of Woden's family with Troy does not exist in English sources, although Sturluson seems to have a later alternative tradition.
Perhaps Geat (or Tatwa) was indeed a primordial giant. Or eponymous ancestor to the Geats/Goths/Jutes. The genealogies all seem pretty muddled.