How do I defend against Nydus attacks in a StarCraft 2 team game?
I will say that your base was harder to get into than your teammates' - you were quicker to bring even a couple of units to the Nydus as soon as you saw it.
Nydus worms, like most Zerg buildings, start with little-to-no health and gain it as they build (up to 200 HP), so an early response, even with just a few units, can make a significant difference. One of my later Nydus attempts into your base was destroyed right as it started in one hit from a Zealot, for example.
I wouldn't rely on Cannons because the Zerg player can almost always find a spot to build the Nydus worm that's out of range of the cannon, unless you spend so much on cannons that you're crippling your army.
Most of the advice to stop Nydus worms applies in general. First of all, you should be keeping an eye on your base no matter which race you are facing, and regardless of whether or not you have scouted a Nydus Network in the Zerg's base. All races have ways of getting units into the back of your base without going up the ramp. Medivacs, proxy pylons, overlords with ventral sacs, warp prisms, blink stalkers, colossi, reapers, etc, not to mention pretty much any air unit.
Denying vision to the zerg player by harassing overlords should be done in general, not just to stop worms.
To help detect the nydus worm (and all other threats mentioned in previous bullet), spread buildings out in your base, so you have vision everywhere. Terrans can spread supply depots, protoss have pylons, and zerg have creep tumours, or overlords to spread around.
Learn the sound a nydus worm makes when it completes. Sadly for us zerg players, the nydus worm announces itself to all players with a loud scream, similar to how everyone hears "nuke launch detected". On the plus side (for us), it only screams as it is finishing. This won't help you stop the worm, but it will alert you that you should be looking for the worm to make sure it's not in your base, or if it is, mobilize some troops to defend.
In team games, consider using the team colors option for the minimap, so your units are green and your opponents are red. This will make the nydus worm stand out in your minimap more than if you are orange and your opponent is yellow, or some other combo of similar colors.
Worms don't have a lot of HP, even when they complete. When they are building, a handful of units can kill it before it completes. I just did a quick test; 3 marines starting to shoot as soon as the worm reaches 50% done can kill it just after it finishes, enough time for only a few units to get out.
Remember that each worm costs the zerg player 100 minerals and 100 precious gas. Each time you kill one before it completes, the zerg is behind on resources. They can also only be building one at a time. (specifically, one per Nydus Network)
What I learned from the campaign is that air units are very effective against Nydus Worms. Air units have the advantage of swiftly moving towards the Nydus Worm, without getting obstructed by the terrain.
So in the case of Terran, you'd use Banshees and keep them near hot spots where they are likely to pop up.
To prevent them from popping up, you first have to scout or scan their base to see if they actually have one. And if they do, spread out your air units as to reduce the traveling time towards the Nydus Worm. Hopefully, you will be able to destroy it before it releases (too many) units.
Also they have to be able to see the area to make it pop up, so scouting with a Raven to detect stealth or hidden units is advised. They can also use Overlords for this purpose and they are always a good target to take down on sight.