What is the optimal strategy to solve Hanoi Solitaire?
The biggest piece of strategy is knowing how to move a pile of cards from one stack to the next.  

The basic algorithm is a recursive algorithm.

To move n cards from stack a to stack b, you need to:


  
  move the n-1 cards from stack a to stack c
  move the nth card to stack b 
  move the n-1 cards from stack c to stack b.
  


To move a stack of three from a to b you need to move the two cards from a to c.   To move the two cards from a to c you need to move the one card from a to b.  Move the second card from a to c.  Move the first card from b to c.  Move the third card from a to b.  To move the two cards from c to b, we need to move the first card from c to a.  Move the second card from c to b.  Move the first card from a to b.

The key strategy is to keep one ordered stack.  When a new card is unearthed, put it in to the stack in the order that it belongs by moving your stack that belongs on top of the new card to it and then moving it to the top of your ordered stack.

This strategy will not likely lead you always to the shortest solution but will lead you to a correct solution.

There are more basic strategies for the Towers of Hanoi peg and disc game on the Wikipedia article http://en.m.wikipedia.org/wiki/Tower_of_Hanoi but I'm not sure how explicitly applicable they are to this game.