Instead of falling into the Battle of Seven Potters, why didn't the Order order a house elf to transport Harry to the safe place?
Two reasons spring to mind:
House-elf magic is susceptible to the Trace.
Witness Dobby’s use of a Hover charm in Chamber of Secrets getting Harry in trouble, despite it not being Harry who cast the charm. If we assume the Ministry could similarly detect a House Elf apparating in or out of Privet Drive, then Harry’s still stuck:
[Pius Thicknesse]’s made it an imprisonable offense to connect this house to the Floo Network, place a Portkey here, or Apparate in or out.
— Deathly Hallows, chapter 4 (The Seven Potters)
We don’t know whether the Ministry would be able to detect where Harry went immediately, but it puts him on shaky legal ground at best. When Rufus Scrimgeour came to give the trio the contents of Dumbledore’s will, he’d also have to bring an Auror with which to arrest Harry.
They didn’t think of it.
Throughout the books, we see wizards disregard the ability of House-Elves (for example, their ability to apparate in and out of places that humans can’t). It’s quite possible none of them thought to ask a House-Elf to do it for them, instead trusting in their own (perceived) superior skills in defensive magic.
A house elf was not part of Dumbledore's plan, Dumbledore wanted Voldemort to believe that Snape is well informed and loyal.
So that Snape will be in a unique position of power so that Voldemort will reward Snape as new Headmaster of Hogwarts (to protect the students of course).
from Deathly Hallows chapter the Prince's tale
“You will have to give Voldemort the correct date of Harry’s departure from his aunt and uncle’s,” said Dumbledore. “Not to do so will raise suspicion, when Voldemort believes you so well informed. However, you must plant the idea of decoys; that, I think, ought to ensure Harry’s safety. Try Confunding Mundungus Fletcher. And Severus, if you are forced to take part in the chase, be sure to act your part convincingly. . . . I am counting upon you to remain in Lord Voldemort’s good books as long as possible, or Hogwarts will be left to the mercy of the Carrows. . . .”
Dumbledore wanted Voldemort to know the correct date of Harry's departure. Dumbledore wanted the Seven Potters incident to happen (to protect the students of Hogwarts of course).
By the way seven Potters and Voldemort's intended Seven horcruxes. Nice coincidence. Seven is a powerful number in magic.