The following is summarized from Danish Tarok - Strategy

Goals

1. Prevent another player from winning an Ultimo.
2. Win an Ultimo (But don't take unnecessary risks; it’s expensive!)
3. Force someone to Lose an Ultimo
4. Win the Last Trick (The usual outcome)
5. Capture Ultimo cards; secure your own
6. Take points.

Roles

Generally, a given deal will sort the players into three roles:

1. The Enemy: the player with the strongest chance of making an Ultimo.
2. The Strong Defender
3. The Weak Defender

These roles may be obvious, or they may not; and they may change throughout the course of the game.

The Enemy

The Enemy is known to the others by making a declaration of Trumps - note if they are avec or sans to know if the risk is of a Pagat or King Ultimo.

If you are the Enemy, you should try for an ultimo if 1) You have a secure ultimo card and 2) your trumps and longest suit together are 16 of your 25 cards, and the other suits are balanced. (Strong side suits reduce this number; weak ones increase it.

The Enemy will want to drive out other trumps, and retain his own until the end. This is usually done by repeated leading the longest suit, and reentering through side suits.

The Defenders

The other two players want to prevent the Ultimo. If possible, they should:

1. Retain a Trump for the last trick, or
2. Drive out the Enemy’s Ultimo cards.

The Strong Defender is the one with the most Trumps. If Trumps were announced, you know how many each player has by arithmetic; if they were not, you are probably the Strong Defender with 7 or more, or the Weak Defender with 6 or fewer.

The Defenders should find a suit the Enemy is weak in, and lead it to draw out his TTTrumps. The Weak Defender should be careful not to lead a suit that also draws out the Strong Defender’s Trumps! When the Strong Defender’s long suit is identified, both Defenders should lead it.

The Defenders should also force out Enemy Kings by leading that suit. Once the Enemy’s Ultimo cards are played, that player is no longer the Enemy.

A Defender who has no hope of an Ultimo himself should play his Ultimo cards early, to identify himself as a fellow Defender.

A weak defender who doesn't know who they're working with you try to conserve both other players’ trumps.

Against a particularly strong Enemy, the Weak Defender can attempt a Misère. This will likely require the assistance of the Strong Defender. The Strong Defender should capture the Weak Defender’s few trumps before the Enemy can make them trump; then lead their long suit so the Weak Defender can throw off any remaining risky cards.

Discarding

Generally the Enemy or Strong Defender should keep their longest suit (though, no longer than 8 cards probably), and balance the rest. A Weak Defender could discards Trumps (if holding 3 or fewer).