Due to the large number of stages I’ll cover a few strategies that work on the contest stages, as well as a few things to look out for on the final stages.
In my experience, the normal stages tend to be won in the first 30 seconds or else they go to overtime. This is characteristic of a map where an objective is quite open but easily defensible by sentry guns, and that’s what the stages are. Your best defence is 2 or 3 well placed sentry guns guarded watchfully by engineers, and a demoman who, if not standing by the point at all times, at least runs back when it comes under attack. A demoman defender is definitely a safe bet during the first 30 seconds where the opposition may try a scout rush, since 2 or more sticky bombs on the control point negates the scouts very efficiently.
The scout rush is worth a mention on hydro, since it can be effective on both the normal and final stages. Have the majority of your team (minus a few engineers and maybe a demoman for defence) go scout, and basically rush the enemy control point. This is especially effective if they try the same tactic, as their defence will have a tough time taking care of all of you. It can be beneficial to all rush the same direction, since any enemies that see incoming scouts will automatically turn around and run to defend their base, and hence the less people that see you the better. If you all stay together, less people will twig to your rush and you’ll face less resistance while capturing.
As for regular attacking, these maps tend to be a slog. It’s important to take control of the map and confine the enemy to their base if possible (see my article on map control), after which you simply have to keep pressing until you have an opening. Since the points are right outside the defenders’ spawn, these openings are very rare, but they usually occur as the result of an übercharge. Once again, this means teams need medics, minimum 1, but really at least 2.
The best classes to übercharge here are probably heavies and pyros, perhaps a demoman or soldier if the enemy point is well covered by sentry guns. Your aim is to force the defenders to flee from the point, which heavies and pyros do very well. Try and coordinate it such that the rest of your team follows the übercharged players to capitalise on the vacated control point. Aside from an übercharge, there is very little that will allow a win in these stages between teams of remotely similar skill. Chances are you’ll face sudden death, so check out my sudden death guide for more on that.
The final stages are always one of two different ones, however they both have the attackers coming down ramps to attack a control point in a pretty open area. For the defenders it is crucial to get defences organised quickly to fend of the first and often most dangerous wave of attackers. This means about 3 or 4 engineers (in a team of 12) setting up sentry guns watching lots of entrances with some kind of view of the control point and demomen quickly throwing sticky bombs around doorways, even if only to scare attackers. The key to surviving is to break up the enemy attack, so deterrence from sticky bombs and pyros is an effective defence.
The rest of the classes are best used for harassing attackers so they are unable to get settled and target specific defences (sentry guns, dispensers, medics etc.). Once again pyros are great for this, and soldiers and heavies form something of a wall that attackers must get through before dealing any real damage. Maybe 1 spy and 1 sniper could help, but generally these weaker classes are next to useless for defending the indoor areas. Most of the defending team should be soldiers, heavies, demomen, engineers and medics, with a pyro or two and perhaps a spy.
As for the offensive team, your main objective is to keep the defenders scrambling. Don’t allow engineers to sit behind fully upgraded sentry guns with wrenches or have medics sitting around corners healing heavies. In the initial wave, take out any buildings engineers are trying to build before worrying too much about the control point. Like most maps, if you are stuck and unable to intrude on their sentry gun defence, an übercharged demoman can level a room full of sentries in a short time period, so look to über these more useful classes rather than the slow heavy or limited ammo soldier.