Map and final wave advice
Every map's wave structure and layout is different, demanding great adaptability from each player and the ability to quickly adjust your tactics. One good example of this is when a bomb's positioned near a reset point. If you have a Pyro in this situation, you should communicate with your team and tell them to hold fire, allowing the Pyro to airblast the next bomb carrier into the pit.
With that in mind, here's the one team setup that I recommend for any expert mission, as it provides the most damage and utility in equal measure when using the suggested loadouts above: Scout, Engineer, Soldier, Pyro, Demoman, Heavy. The most interchangeable class among that bunch is the Soldier, seeing as they become less effective when faced with Giant Deflector Heavies, which are particularly prevalent on Mannworks. In these situations, it's perfectly acceptable to bring a second Heavy.
The first wave of any expert mission is always difficult because you can't afford many upgrades. However, if you can get up to at least the penultimate wave within an hour then you know you have a solid team. Once you get to the latter waves, the obvious advice is to hold onto your initial frontline for as long as you can and spend as little time as possible fighting for your life outside the spawn rooms. Here's some tips about each map as well as how to tackle the final wave of each expert mission:
Coaltown - Cataclysm
Coaltown is arguably the most accommodating map for expert missions. You have two very accessible bomb reset pits and the robot entrance points are all close to each other. This means you get a very handy bottleneck at the start of each wave that a Demoman can easily cover with stickybombs. This helps to dampen the difficulty of the final wave in which you'll face six tanks and four giant Heavies, punctuated by a lot of Uber Medics attached to various smaller robots in between.
At the start of the wave you'll be faced with five of those tanks in quick succession. The first one is easy to deal with, but when the second tank rolls in you'll also be faced with a lot of Scouts, all with their own Uber Medics. It's at this point that you need a Demoman to take care of as many of those Medics as possible while the rest of the team focuses on the remaining tanks. There will inevitably be some Ubered Scouts running amok, but you can use the large sides of a tank as cover from their fire. When Snipers start to spawn, it's best to have your Engineer wrangle their sentry and deal with them while the tanks continue to be focused on by the rest of the team. Even if you are pinned back by the time the fifth tank comes in, it's possible to move forward as long as you do so together. If the robots are taking the right hand path on their way out of the entrance, having a Pyro airblast the bomb carrier into these pits is immensely helpful as it allows for more focus on killing the tanks.
Before the end of the wave, there's a surprisingly lethal pack of Buff Banner Soldiers, all using a Direct Hit, who try to ruin your day. If you have either a Heavy, Pyro, Soldier or Demoman available with Uber canteens then it's a good idea to use these and mow them down. Then you're onto the final tank and the four giant Heavies who accompany it. Fight them from the roof of the middle house, taking cover when necessary and using crit canteens to burn them down quickly as they have no Medics with them. This should give you ample time to destroy the final tank - using more crit canteens if necessary - to complete the mission.
Mannworks - Mannslaughter
Mannworks is a much more challenging map than Coaltown. Robot entrances are far more spread out, so they're much harder to cover. But if you have a Demoman then this is why the Scottish Resistance was recommended earlier, you can lay seven bombs at each entrance as opposed to just four. However, if you'd rather have two Demomen using the regular Stickybomb Launcher in place of a Soldier or Heavy, then have at it.
The final wave of Mannworks is horrible. Eight Rapid Fire Demomen, eight Rapid Fire Soldiers (all with their own Uber Medics) and four tanks are the biggest causes for concern, but the 60 Pyros as well as Spy support bots are no pushovers themselves. How well you deal with the wave is mostly dictated by how well you deal with the initial attack from the Rapid Fire Soldiers. Have your Engineer build their sentry on top of either the quicklime sacks - as seen in the above screenshot - or pile of wooden planks outside the house near the robot entrances. Building up there allows them to be fully covered from damage but still allows them to repair their sentry from the very high damage these robots can deal. It's crucial that you don't allow many Soldiers to be ubered by their Medics, otherwise they could tear through your team, so your Demoman will need to be on the ball with catching these Medics as they spawn. If your defense can hold off this first batch of Soldiers and remain mostly in tact, you're very well placed to deal with the rest of the wave. Burn down the Rapid Fire Demomen, using either Buff Banners or the Fan O' War to help you and the rest of the wave is comparatively small fry. Stick together, watch each others backs when the Spies appear and airblast the bomb carrier into the large crater that separates the two lanes. When the final two tanks come towards the end of the wave you'll still have a lot of Demoknights to contend with, but these can mostly be dealt with by your Engineer and their sentry. Again, you can use the tanks as shields so that the Demoknights can't see you. Once the tanks are down, fight off the remaining Demoknights to finish the mission.
Decoy - Desperation
Decoy is a compromise between Mannworks' awkwardness and Coaltown's bottleneck design. Most robots will enter under the initial bridge, but the occasional blighter will spawn on top and make their way around the upper level of the map. This is what Snipers do most often, so the best way of dealing with them is to have an Engineer wrangle their sentry and pick them off before they can damage your team. There are two bridges over a large hole before the hatch which acts as your reset point for the bomb. If possible though, try to airblast robots into the hole before they get onto either bridge because one of them has railing on either side which giant robots can't be blasted over without great hassle.
While preparing for each wave, have your Engineer build their sentry and teleporter on the middle house's roof. You should have the dispenser placed on the corner of the big building in front of the house, ahead of the bottom of the ramp. This means a constant ammo supply for the classes on the frontline which is crucial for success in the latter waves.
The final wave is a deadly one. Two tanks, four giant Heavies, 12 Rapid Fire Soldiers and 12 Super Scouts. The start of the wave is simple enough, you get one tank on its own which allows everyone to focus their attention on it. It should die before it's even allowed to turn a corner. There's a brief lull in activity after this in which only Pyros and Heavies will appear with the occasional Uber Medic. If you're a Soldier, use this opportunity to prepare a Buff Banner charge for when the giant robots start to appear and fight with the rest of your team at the dispenser (minus your Engineer). When the giant robots come, they come in groups. First you'll be faced with giant Heavies and the Rapid Fire Soldiers. Thanks to the layout of the map, your Engineer and their buildings should be protected by the frontline. To ensure safety, keep using the Buff Banner whenever available and throw Mad Milk onto the Heavies, as they soak up the most damage and will therefore heal the most to those who attack them. This forms about two thirds of the wave.
The final third is when the Super Scouts enter the fray and more Uber Medics arrive with giant Heavies. It's very important that the Scouts are juggled in place by a Pyro's airblast, allowing the team to kill them off quickly, otherwise they can slip past you too easily and end the wave. If your Pyro's dead or you don't have one on your team, it's a good idea to have your Engineer move their sentry to the end of the bridge that the robots are supposed to cross. This, combined with some damage from the rest of the team, should be enough to see them off. You still have several Rapid Fire Soldiers and a couple of giant Heavies to take care of too. Your Demoman should, as always, consider it a priority to deal with the Uber Medics. This allows you to plough through the remaining giant robots with the aid of canteens. With a few giant robots still on the map, the second tank enters, but you can afford to leave that until you've dealt with the remaining enemies. Once they're down, focus all fire on the tank to bring it down and end the mission.