AD698 Half bridge LVDT circuit
Circuit I used is exact one in page 6 of AD698 datasheet.


No it isn't - you haven't got R4 connected in your circuit to pin 23. This affects the offsets and I don't see one diagram in the data sheet that has this resistor omitted. The data sheet says: -


  Selections of R3 and R4 permit a positive or negative output voltage
  offset adjustment.


Having only one of these fitted means having a big offset!

Also, are you supplying a mid-point 0V to pin 21?