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?