Would my sentences sound off?
I'd like to do that.
But the students haven't learned the pattern "encourage (person) to (do)" yet.
So I didn't put "to do something" at the end.
While I agree with the others that encourage is usually paired with something, your examples are perfectly fine and do not sound off. The reason is that the type of encouragement is implied and doesn't really need to be stated explicitly. The reader can fill in the blanks.
(a) Whenever I am depressed, my parents encourage me.
==> it's implied that your parents are encouraging you to feel better about yourself.
(b) Letters from my wife always encourage me.
==> it's implied that the letters encourage you to feel better or try harder.
(c) I'm always encouraged by letters from my wife.
==> It's implied that you feel better or try harder or don't want to give up when you read these letters.
(d) I thought I couldn't beat him. But your words encouraged me.
==> It's implied that the words made you try harder or believe more in yourself.
(e) As his father, I've always encouraged Tom.
==> It's implied that the father has encouraged Tom to do
something such as following his dreams.
In summary, your sample sentences are perfectly fine for this classroom English lesson.
I hope this reply of mine has encouraged you.