Grand Master Yoda is the first event character, and unfortunately the weakest. That being said, Yoda still has a place in the competitive arena metagame as a useful support character. Lately his role has been restricted to solely Jedi teams.

Lead

Jedi allies gain 30% Tenacity, gain 30% Turn Meter whenever they Resist a debuff, and whenever they suffer a debuff they gain Tenacity Up for 1 turn at the end of that turn.

Bluntly put, QGJ is still only a relevant character because of his leadership. However, this leadership ability is one of the best leaderships in the meta right now, enough to make an otherwise mediocre character not only viable but a key component of a top-tier team.

The speed bonus is crucial. This adds a massive amount of effective TM to your team (or at least your Jedis) and can keep pace with other TM leads like Rex or Darth Maul. The Offense bonus is notable, ending up at ~20% extra damage. As Jedi are rather weak attackers in general, this Offense boost is quite welcome. Finally, the Foresight boon is exceptionally useful as well, particularly against the AI. Automatically dodging attacks is simply fantastic, and regaining it regularly is a great boon.

Non-Lead

For the most part, Yoda’s purpose is to use Battle Meditation. This is cruicial in providing Jedi teams with Tenacity Up. Jedi teams are particularly reliant on buffs, so debuffs like Buff Immunity and Skill Block are especially bad for them. Further, the extra Foresight really helps.
Technically he has other abilities, but oftentimes those can either be more of a detriment or have tiny effects. His basic will get you into a lot of trouble. Thanks to its weak power and the heavy anti-crit & counter-attack meta, you’ll often find yourself regretting his attack.

His two other specials aren’t much better. His AoE attack, Masterstroke, is one of the weakest in the game, and while stealing buffs is a neat trick, it rarely coincides with a useful result. Theoretically it should lead into a Battle Meditation. But stealing useful buffs, keeping them, and surviving to spread them is a tall order for yoda (Get it, tall order…).

Unstoppable Force has some niche uses. You really are going to use it for the stun. The turn meter reduction isn’t reliable enough between the mediocre proc rate and Yoda’s lower potency. It’s admittedly rather difficult to keep the stun up against the popular cleansers, however.

Synergies

Yoda has some interesting synergies, to say the least. His most obvious use is to protect characters that have weaknesses to debuffs, and to protect fragile characters with frequent Foresight. Since those are hopefully self-evident I’m going to move on.

His more interesting synergies are through his other specials. With his AoE he can steal strong buffs which can be an interesting counterplay to Rogue One teams and the like.

With unstoppable Force, he can pull off a semi-reliable stun if the target is below 100% health. Normally that means the target is going to die shortly afterwards. However, there are ways to get around this. Emperor Palpatine’s NAME HERE means that all characters will be below 100% health. This allows you to pull off a clutch stun.

Mods

Speed. Moreso than almost any other Jedi, Yoda relies entirely on his speed to be useful on an arena team. Really his sole job is to provide Battle Meditation as early and as often as possible. After that, if you have a choice, survivability is an okay option. This won’t really do as much, however, as Yoda’s base survivability stats are so low. It’ll be hard to notice the difference.

Avoid crit chance like the plague. While you can get a tiny amount of extra damage, it’s not worth triggering the opponent’s anti-crit abilities. Yoda’s damage is so small that it’s a bad trade.

Don’t fall into the trap of modding potency. Yoda only has one skill that requires it, and it’s so rarely a factor that it’s not worth the stats.

Counters

Countering Yoda is unfortunately rather easy. His tiny effective health pool means he doesn’t really stand up to much abuse. Boba Fett’s Execute is an excellent way to snag a quick kill. Just about any amount of AoE spam can often kill Yoda on accident.

As may be expected for a Jedi, Yoda is buff-dependent. This means dispellers and Buff Immunity are especially troublesome for Yoda. Look to characters like B2 to give him a hard time.