What strategies should the Protoss use against mass Medivac/Marine/Marauder?

Solution 1:

As a Protoss, you need to focus on a few objectives when fighting against bio Terran:

• Don't die (just yet). Kind of a no-brainer, but the idea is not to move out and overextend until you are ready. In mid-game, bio Terran has superior map control, have higher supply than you, and will crush you if you move out. Play defensively, try to secure a third base, and move out only when you have enough high-tier units. Scout with observers, hide strategic Pylons around the map for scouting drops and occasional Zealot warp-ins for harrasing expansions.
• Win every battle decisively. Since the Terran will have map control, they will (should) generally expand faster than you, and be able to remax almost as quickly as a Zerg. For this reason, you will have to win every battle decisively, otherwise they will just crush you with the second wave of reinforcements. Choose your battles and don't attack in an unfavourable position.
• Hurt them after you win an engagement. Terrans are very mineral-dependent, and will have heavily-saturated expansions. Destroying one or two of their mining bases will not make them happy -- that's why you need to win decisively to be able to counter-attack quickly and score a few free SCV/CC/mule kills. If they have too many bases, you could also attack the main and destroy unit-producing facilities, hopefully crippling them enough to allow you either to expand safely, or to finish the game.

Some things you need to be doing:

• Keep up with upgrades. I can't stress this strongly enough. Maxed out vs. maxed out, Terran will probably win in the majority of the cases unless you have some aces up your sleeve (more on this later). Get that double Forge and chrono-boost the hell out of the Gateway unit upgrades.

• Good positioning is key. Large open spaces favour Terran as they allow them to develop that sick concave that will roll you over and prevent you from getting the most out of your splash damage. Cramped spaces, chokes and ramps are in your advantage, use them early on to deny them a good battle position, or just to stay alive. Early-game sentries are a must for crowd control, but don't invest too much in them after this, there are better things to spend your gas on.

  Only one botched battle is enough to lose the game if your high-tier units die, so don't get caught out of position, and don't overextend to pokes and baits. An eager-to-kill Protoss is a dead Protoss.

• Get some splash damage. You absolutely need this. No amount of zealots and stalkers will help against stimmed Terran army if you can't kill them quickly enough. Your first choice should be Colossi -- the Terran probably won't be producing Vikings just yet, and be getting Medivacs instead. Getting a critical mass of 5-6 Colossi (with sufficient Zealot meat shield and some stalkers to take down the Medivacs) should allow you to crush them in an engagement. Which leads us to...

• Force tech switches. The bread and butter of PvT, IMO. After winning the first engagement with your Colossi, your opponent should start getting Vikings (otherwise they are pretty much dead if most of your Colossi have survived). Which is exactly the time you should be getting High Templars (Psionic Storm works wonders on a group of Vikings clustered up for sniping a Colossus), and ramp up your Stalker count. You'll likely lose all your Colossi at one point, but if you managed to make your opponent overcommit to Vikings, you should not be replenishing them. Instead, gradually add more Archons to the mix, especially if/when they start making Ghosts to counter your Templars. During the entire game, you should be the one telling them what and when to build, and prepare accordingly.

• Shut down any drops. If you play defensively, the Terran will naturally try to do drops. Just one or two successful drops on their side can decide the victory in their favour, so keep on your toes. Get quick Blink, scout with pylons and observers, and patrol around your assets.

• Keep your minerals low. You are very gas-dependent as a Protoss, especially when you are building Colossi and Templars. You'd probably have some minerals to spare, which you should invest in production facilities and zealots. Zealots with good upgrades and charge will buy enough time for your heavy hitters to melt their squishies, and will prevent them from reaching your high-value units. If you have a lot of minerals stashed, you are at a higher risk to die due to a timing push from the Terran before you have built an army composition that can crush them.

Some other exotic things:

• Force scans. That is, build DTs. You don't need them for harassment, you will use them either defensively (to shut down drops), or to force scans. Remember, every scan they have to make costs them around 250 minerals (one less MULE), and when they are so mineral-dependent, every little bit counts. You'll need superior defense if you build DTs, as you'll fall even further behind on supply and will lack "real" units to engage the enemy. So make those DTs count.
• Keep them busy. It's difficult enough to keep up with all this, but if you can manage to spare some extra APM, play around with the Terran around your base. Pretend to be attacking, force a stim or two on half their army, drop a Force shield or two, maybe even kill a bunch of units, and then retreat. If you do this without major losses on your part, your opponent will become increasingly frustrated and is more likely to overextend and attack you unprepared.

PvT is all about quick upgrades, tech switches, and strategically planned engagements. You need to be controlling the flow of the battle in order to be the last to gg in the end.

Solution 2:

You'll need splash damage against this kind of army, because otherwise the Medivacs will heal up the army so fast, you won't stand a chance without hitting a lot of the bio units at once (hence splash damage).

Colossus and/or High-Templar with storm are great choices vs. bio. Maybe mix in some Archons (they also deal splash-damage and are great tanks). Use sentries to slice off parts of the bio ball or prevent them from running out of your storms. Colossus is probably a bit more beginner friendly than Templar.

In any case, you should have a large gateway army with good upgrades that can serve as a buffer between the MMM-ball and your splash-damage units.

Solution 3:

In the very early game, usually before Medivacs, good Sentry usage is key: you don't want to allow the Terran to kite your units. Trap the escape route with forcefields then block him in with Zealots. Zealots (minerals) are expendable, but everything else is much less so- you don't want to lose gas units so retreat with them early enough to escape if a fight looks lost. In full out battles, be sure to use Guardian Shield to seriously cut into his damage.

MMM is most dangerous in TvP before you have splash damage (Archons, Colossi, or Storm) and during that time I personally find both Immortals and Chargelots to be very effective. They tank a ton of damage and can deal great damage against Marauders and Tanks. Make sure to focus Immortals on proper targets during battles; with 6 range it's much easier to do so.

In midgame, Upgrades are also extremely crucial, you absolutely need to be ahead of him in upgrades at this point because you don't have the splash damage to just melt stuff that comes within range. Chrono Boost the hell out of those Forges and the Twilight Council.

In the lategame with 200/200 3/3 armies, it all comes down to EMP versus Feedback/Storm. Use observers to keep an eye on his army and ensure he doesn't get any significant cloaked EMP's off, and send single High Templars to feedback and kill idle Ghosts from high ground or fog of war. Keep your army and especially your energy dependent units somewhat spread out in order to minimize the damage an EMP can deal to it.

Protoss, in my opinion, has an enormous advantage in these lategame engagements if they prepare properly: with tons of Gateways you can reinforce with 30 supply of Zealots in 5 seconds, or a similar supply of Archons in 10 seconds.