First, let's clarify something: Attack is your main action. The other actions are more situational, so it's expected that Attack is going to be used way more often than not.
Threaten your squishy PCs. Put a huge melee fighter close to your Wizard (or sorcerer, or w/e, you know who is the squishy one). Make him a threat that will be extremely dangerous if they choose to fight close-range and take opportunity attacks from him, while disengaging and outsmarting will make the fight easy.
In a homebrew campaign, I had a Fighter Kobold (it was a Kobold-themed campaign...) that fits this very well. His normal action would be an usual melee weapon attack, but his opportunity attack (more like a reaction attack that had the same mechanics as OAs) would be devastating (3x the usual damage).
Note that this is more about forcing them to use the Disengage than encouraging them. But it works.
Again, note that Disengage is a very specific action. It's not going to be used that often.
I have seen my players use dodge mostly in two situations:
- Melee characters in a fight against ranged creatures/NPCs. Sometimes, instead of dashing to get closer faster, they would prefer to Dodge so they can get closer more safely.
- The "Tank" is being targeted by a mob (or anyone, but that usually happens to the tank - if a mob is targeting the Wizard he might as well be dead. Rather, I hope he is teleporting away). The more monsters are focusing in one person, the more attractive is for that person to use Dodge. Attack will maybe get rid of one creature, while Dodge will save him lots of damage while giving time for the rest of the party to do the damage.
From that, the most likely scenario for Dodge to be used is combining both - lots of archers firing at someone. Dashing might get him faster, but he might as well be dead then. Dodging will mitigate the damage and get him alive to the other side.
Help is obviously going to be used alot by familiars. For PCs, it will be used if there is a great difference between the damage done by the characters. Honestly, I find the Help action bad in combat for some reasons:
- It only helps with Attack Rolls - and only for the first attack roll.
- You need to be on melee range.
The first condition means that helping your Fighter won't increase his DPS as much because it won't profit in each of his Extra Attacks. It also means that helping your Wizard that is going to cast a Fireball does nothing.
The second condition means the people that do low DPS without using resources (i.e. spellcasters without using spell slots) and would like to Help instead of using a low-damage cantrip have to be where they don't want to be - close to the enemies.
The way Help works, I feel it's more about non-combat scenarios.
However, you can create scenarios where there is a huge difference on damage. The main scenario is giving Immunity to Physical (slashing/piercing/bludgeoning) damage to the enemy (rather, putting them against an enemy with these immunities). The Fighter/Barbarian/Rogue of the team will spend more time Helping the spellcasters to do damage than trying to do damage themselves.
Note that this might make the Player feel bad about that combat, as shown here: As a Barbarian, how can I contribute to fights against slash-immune creatures? - but "Use the Help Action" is one of the answers of this question.
Bonus for Help:
After reading one of your comments
But the mechanical benefit is so weak that my players feel like they can't afford to make those choices, even when it makes sense from a story perspective.
Make the key ability check mechanically relevant. For example, I've had a Golem that had 4 Small-towers "buffing" his AC. The towers would have to be destroyed so the Golem could actually be damaged. It's an easy "translation" to, instead of destroying the towers, the PCs having to deactivate them through some kind of skill check. The faster the Wizard passes these Arcana Skill Checks (or whatever fits the best your narrative and party) to deactivate the towers, the faster they can actually start hitting the Golem. The Fighter has a bad bonus on Int and no proficiency on Arcana, so he's way more useful giving Advantage to the Wizard than trying to deactivate himself.