Did Ned Stark have any uncle or aunt?

No.

I asume that important families like the Starks would keep in touch with their greatuncle and greatuncle's grandkids; cousin and 2nd cousin and 3rd cousin and so forth. So there would be a lot more Starks around than just the 7 we saw (like the Freys or Lannisters).

There are probably some descendants of offshoot branches from the family tree floating around the north, most likely in White Harbor and Barrowton.