House-Elves wear things like pillow cases and tea cozies, because they are not allowed clothes. If a house-elf's master were to give them any clothing, even a sock, the elf would be free to leave their family forever. At the end of Chamber of Secrets, Harry tricks Lucius Malfoy into freeing his house-elf, Dobby.
Most House-Elves would be offended if given clothes, for it would mean that they had failed to properly serve their master, but some (like Dobby) enjoy being free. However, Dobby still doesn't want to be paid too much.
Hermione Granger was horrified at the way house-elves were treated and started the Society for the Promotion of Elfish Welfare (S.P.E.W.) to help house-elves. However, the house-elves don't seem to want to be helped. Hermione hasn't given up hope.
J. K. Rowling's characterization of a House-Elf owes a lot to the legends of brownies, and also to the traditional figure of a hob-goblin, a half-tamed, amusing but tricksy goblin of the hearth (the "hob"), often euphemistically called "Robin Goodfellow" or Puck.