What are some basic strategies for Labyrinth?
A few tips:


Static tiles are more stable (duh!), so going there is a bit more predictable. If you have goals on those, they have lower priority.
Static tiles are more stable (again), so staying on a static tile at the end of your turn will assure you you are at the same place when you begin the next one.
Manhattan distance (dx + dy) may be important because being close to a goal makes it easier to reach if you are not sure of what the board will look like on your next turn.
Don't forget to use the "shortcut": if you stand at the edge of the board and you are pushed out, you teleport to the other side.
Having a large reachable zone at the beginning of your turn allows you to adapt easily: if you can go to a lot of places, you can change your mind when trouble arrive.
Play the anti-game. Even though I would never recommend that to any living player, as your goal here is clearly to win and not at all to have fun while doing it, crush your opponents completely without mercy! Sometimes, reaching your goal is more complicated that putting your opponent(s) in a tricky situation. Keep in mind who is about to win and don't be nice with him (or should I say "it"?) Everything that I said higher can be applied negatively to the others.