strength of move/ rating association for move choices
The analysis engine gives you the evaluation of every position.
The standard way to measure what you are talking about is "centipawn loss" - you take the evaluation of the best move, and subtract from that the evaluation of the move you made.
It's easy to do in the postgame analysis here.
http://chesszen.com analyses moves and estimate ELO.
That URL leads to a parked domain, did you get it wrong?
http://chesszen.com analyses moves and estimate ELO.