Yes. They sound odd. It's the "you. . . if you . . . me" part that's awkward.
Either omit "you", like this,
Would you mind typing a letter for me?
Would you mind lending me your pen?
or replace "you" with another pronoun, like this,
Would you mind if I typed a letter for you?
Would you mind if I lent you my pen?
"you" works if you change the verb to a modal, like this,
Would you mind if you couldn't do it?
Would you mind if you had to do it?
- For Teachers