The Phoenix of Tichu is arguably the strongest single card, but it comes with a hefty cost. It compliments almost any hand, and certainly never hurts it. Use it to make a run, a three of a kind, or simply beat that lone Ace that was played. It can be the glue that holds your hand together. This versatility is offset by its -25 point value. And unlike the Dragon, if you win the trick the Phoenix will come to roost with you.
It pairs well with the Mah Jong, improving the odds of an initial low card run. While it can't be used to explicitly fulfill a wish. (e.g. If someone wishes for a 5, I do not have to play the Phoenix as a 5). However, if there is a wish to be fulfilled and you have the card that was wished for, but need the Phoenix to play the same denomination (i.e. a straight, or a pair, etc.), then you must fulfill the wish.
Imagine the glory of playing the Mah Jong as part of a five card run, wishing for an Ace, and watching as the trick is not taken. Then you lead out with your triple 7s and watch as your opponent plays two Aces and the Phoenix.
As with the Dragon and Dog, having knowledge of who has the Phoenix is boon. After all, once the Dragon is out, the Phoenix can be the highest card. As such, I consider passing the Phoenix as a viable default. If my hand has lots of pairs, the Phoenix can likely help my partner glue together a run. If, on the other hand, I have lots of singletons, I'll keep the Phoenix.
Never pass the Phoenix to your opponent. If you can't make use of the Phoenix, then your partner can…I promise.
One thing to keep in mind, as you are playing out the hand, is that you can give your opponents the Phoenix points by simply holding onto the card until the hand is done. This tactic is best employed when your partner has gone out first. The reason being that if your partner goes out first, then your tricks are safely yours. But don't slack off if there is a chance for you and your partner to go out 1st and 2nd.