The German Language

[abaris]

but I see few, if any, similarities between English and German words.

How did that come to be so?

Information is literally the same word.

Bed - Bett

House - Haus

Murder - Mord

sleep - schlafen

go - gehen

learn - lernen

And many, many more. I found it pretty easy to learn English with German as my first language. It was much harder with French and I've already forgotten most of it over the years.

Also, maybe without you knowing it, you're using German words in America that have been kind of naturalized: Rucksack or Kindergarden (Kindergarten).

...plus the things taken directly from greek and latin by the learned, plus the stuff Shakespeare just made up because he felt like it

Medieval German is actually much more similar to medieval english than any contemporary comparison. Till the first vovel shift, which happend somewhere between 700 and the year 1000. Probably a very gradual process.