The sun as you see is as it was 8 minutes ago, So suddenly if we could some how manage to push the sun farther away. Then would we still continue to orbit sun for the next 8minutes in the same path without having a feel of changed gravitational field? This probably seems to be possible, reason as why I feel so is even force of gravity can't reach us faster than speed of light. OR if we go by Einstein's model of gravity Curvature of space, then we should be in a different path of curvature instantaneously, we should have feel of changed gravity.

The force of gravity from the Sun on the Earth is so slight compared to that generated by the Earth's core is that there would be no measurable difference. The more you push the Sun away, however, the more we would feel other consequences. I am not familiar with a method of measuring the "speed" or gravity, and it is much less understood than light.

The question here is "what is the speed of gravity".
Depending on the source, it is "C" (the speed of light in vacuum), or "infinite".
The last insights on the question are that gravity propagates at the speed of light though. This means that if the sun would disappear, earth would indeed continue to orbit during 8 minutes.
See the article in the new scientist on:
http://www.newscientist.com/news/news.jsp?id=ns99993232