General Strategy
You will want to stay towards the outside of the fray of the other three. You never want to get boxed in between two characters as Snake. If you do get boxed in, excessive shielding almost always works in that situation. Or even full hopping out of there. Be careful to not let your shield break.
From the outside position, you'll want to simply chuck like one grenade at a time towards the central fray to add damage, but to be safe as well. This is because people will likely come to attack you once in a while and you need to be ready and not caught holding a nade. Try not to simply stand on the opposite end of the stage for too long because that's pretty obvious your avoiding conflict and people will start targeting you. Better to keep close to the fray, but always just outside of their range.
People in the center between characters will likely favor trying to roll behind you. As an extra precaution assuming people will roll behind you and try to maintain a roll's distance between you and your opponent. This way if they do roll, they do not end up behind you. If you get a grab, do not go for a dthrow, but rather throw them towards the others. You increase the likelihood that they will get targeted by other players and attacked.
If you get stuck on the ledge and a ton of people are there, you need to choose a safe option for getting back on. Typically, falling down and regrabbing the ledge for invincibility helps wait out the fray on the stage. After it dies down, you can stand back up from the ledge. If people are starting to get hit off the stage or fighting on near the ledge while your there, rolling from the ledge or standing up into shield is a good option.
Overall, I am advocating you want to keep a low profile and avoid being hit too often and let the others do most of the damage for you. That way when it gets down to singles, you have the stock or percentage to hopefully win the fight.
Items
Sadly, with items on a bit of randomness is thrown in and you might have to readjust priorities from time to time. You want to try to claim like one dragoon piece if it shows up. The goal is not necessarily to go out of your way to collect them all, but rather prevent it from being assembled. If they happen to be near you without risking it, then go ahead and get all of them.
Similar thing with the smash ball. When it first comes out, no attack will break it right away. It takes a few whacks. Let the others get like 1-2 whacks at it, then you come in and get the final whack at it. If the smashball has not been hit for say 10-15 seconds, then a single strong attack will break it right away.
Hammer is awesome, but you cannot second jump or use cypher with it on. If you get hit offstage while using this, your dead. Other items are actually really bad to use for Snake since his tilts are infinitely better at swatting people away. Better to grab an item and throw it at people right away or throw it off stage. Beware through of people with reflectors if you do this.
The assist trophy will make you completely vulnerable until you actually go through the whole animation. Say you partially start doing it, then you get hit into the air, the next time you touch the ground you restart the whole thing. So, you could potentially get repeatedly hit until you finally get it off.
There is some judgement with using items, but I think that something you learn if you play with them a lot.
