Actually Bry, there is little or no connection between Quenya and Old English. The two languages which influenced Quenya most were Latin and Finnish, though it actually resembles neither language, JRRT simply took some of the grammatical and orthographical structures from both and combined them with many other ideas of his own to create a unique and new language.

Welsh was a major influence on his other Elvish language - Sindarin.

Old Norse forms were used by JRRT to represent the northern forms of Westron - eg the Westron names for the Dwarves (Balin, Gimli, Gloin etc) and Gandalf's name. OLd English, or rather its Old Mercian dialect, was used to represent the language of the Rohirrim and Gothic forms were used to represent the ancestral form of that language.

This does not mean the Rohirrim "spoke Old Mercian" or the Beornings "spoke Old Norse", just that JRRT used these languages to represent these forms of Westron and their relationships to each other.
Cheers,

Thiu