Unlimited Hazama isn't as bad as he appears. For starters, stop jumping. Unless he is on the ground, it is not safe for you to jump. It won't really net you any advantage. Also, despite being a zoning character, he doesn't actually zone all that well, so don't be afraid to play from a distance.
If you are playing as Litchi (you should play as Litchi, by the way. She is the best and all other characters pale in comparison), you should use shishin/four winds (41236D with the staff down). A lot. It is great against unlimited Hazama -- particularly when he's on the ground -- because he has no defensive game and attacks aggressively. 6B[m] is also excellent against Hazama because it has a fuckton of reach. An easy combo you can do off of 6B[m] counter hit is 6B[m] dash 5B[m] j.B[m] j.c[m] dj.B[m] j.C[m]. If you don't know what any of that means, I can clear it up for you. The itsuu moves are also excellent against Hazama (41236D with the staff followed by A, B or C -- A is an anti-air, B hits in front of you, C hits diagonally and down) because they have long reach and do a lot of damage. They're also safe if he blocks them, so you can do more things afterwards should you so choose. If/when you get meter, throw the staff as close to him as you can get it and use kokushi/thirteen orphans. The computer's inability to block makes this basically free damage; while it's hitting them, feel free to wail on him as Litchi. Moves in the air are best. RC is very difficult to use as Litchi so don't bother. Finally, remember that you are playing against a computer -- if he gets close, don't hesitate to use Tsubame Gaeshi (623D with the staff). It beats every offensive option he has.
Tager is hilariously easy as Litchi. Jump backwards and use 6B[m] followed by 6C[m]. Don't throw the staff, don't be aggressive. Just create as much distance as you can (Litchi has a double backdash on the ground - Input it with 447) and jump over him if you have to. Once you've created enough space, throw out 6B[m] followed by 6C[m]. You don't even need to follow up those moves, but you can if you're feeling brave. You can delay the 6C[m] a little bit to punish a lot of options as well, although that's more applicable to playing against actual people than it is for playing against the computer.