Hooking up a 3 wire load cell and measuring the output on an ADC
When I put pressure on each of the load cells I see a deflection which
  goes positive for 2 cells and the voltage goes decreases(but not below
  0 (stops at 0) ) when I put pressure on 2 other cells.


If you have scenarios where a weight over two of the load-cells increases voltage but the same weight over the other two decreases the voltage then you need to swap the two end wires of the two load cells that send the voltage negative.


  how exactly do I read these inputs from s+ and s- using an ad620 or
  LM307?


Use this circuit but you might need a negative voltage supply to make sure the AD620 input voltage common-mode range is not infringed - read the data sheet.