Saxon isn't "old English, Saxon is Germanic, from when the vikings ruled large portions of England.
Then of course there were the Latin words that got mixed in, and the several varieties of Gaelic and Pictish.
What makes it hard for foreigners to learn English is that it is the most bastardized language on the planet.
Actually Tom, yes, Saxon is Germanic, but it is not Norse.
The invasions (of major groups at least) in England started with pre-Picts, then Picts, then Celts from Dalriada (Ireland), then Romans, then Saxons and Angles (both from NW Germany, SE of Denmark) - BTW, the Saxons were so-called because of their weapon, the saxe, sort of a long knife not quite a sword.
After the Saxons and Angles invaded, they were followed by various "Danes" (Norseman) who conquered most of the England we know today - save Wessex in the SW, from which came the great king, Alfred (aka Alfred the Great, the only English king to ever be granted that appellation). King Harold repelled a sort-of-civil war invasion by more Norseman (the last Norse invasion BTW), only to have to hustle down to Hastings a few weeks later and be killed by William the Bastard (aka Conqueror) - a Norman.
Damn, I have tons of totally useless information at hand. Was there a bet on this?

OE does draw from all of the cultures pre-Norman invasion, which introduced French and converted English to the so-called Middle English IIRC.