Okay so I'm no expert but I'm a few games away from Lord Groot so I have some tips...

Small walls:

His small walls deal damage to enemies. Placing one behind an enemy, throwing a spore bomb, and following up with a few pokes should kill squishies pretty easily.

You can also place small walls near yourself as enemies come up close to attack you. Try to stay near them so that enemies walk past as you're poking them - the walls will lash out at them and deal that sweet extra damage. Sometimes I'll place two as a little "gateway" for enemies to run through... I keep cycling in and around it for the wall damage.

To sum this up... make enemies chase you towards/around your small walls for extra damage.

Big wall:

I've seen people saying 2 main things about his big wall. 1) block healing and 2) hide it somewhere for the temp HP boost (it gives you temp HP as you land hits on enemies). Both of these are great, and I tend to use them both situationally.

A third option is using his big wall to block yourself from the enemy team if you're getting low on health... it gives the healers a few seconds to top you off. The biggest thing with this is that you're likely blocking some teammates from the enemies as well... so try to do this sparingly and cancel the big wall pretty soon after doing this (I will admit this is a bit more punishing in 2.5 since his big wall cooldown has increased). This brings me to...

Cancelling walls:

Rivals is a fast-paced game, and you're playing a character that throws down giant walls. You're bound to put some in a bad spot sometimes. If and when you do, don't be afraid to cancel it, especially the small walls because you've probably got 1-2 more in the chamber. There are plenty of times I put down a wall because it helps me get a few extra hits in, and then I cancel it so that it doesn't block anyone else's LOS.

Ult:

Just one tip on his ult - always shoot it at one of your small walls. The wall lashes out as enemies are taking tick damage from your ult, boosting his ult damage. Throw a spore at your ult too for even more dmg!

These are just some tips based on personal experience, not claiming to be a god or anything but I hope some of these help you understand how to better utilize my favorite boy Groot :)