There are two ways to adjust to "weird" serves and shots. One is to practice against every single one of them, until you are comfortable against every single one of them. Since there are a huge number of ways to serve or hit a ball, and anything that's not "orthodox" can be considered "weird," this would mean basically turning your practice sessions into just practice against these weird shots, as opposed to developing a foundation to your game. This would be a mistake.
While you should sometimes practice against seemingly weird serves and shots you might see in a match - especially the more common ones - it's better to focus on developing a strong foundation to your shots. This allows you to develop complete command over your shots. When developing a shot, but before a player really has command of it, he mostly does the shot robotically, meaning he can do it against the same incoming ball over and over, but can't adjust to anything different, i.e. "weird." But with practice, you develop command of the shot and it becomes so ingrained that adjusting to different shots becomes easier and easier. But it takes experience - not against every possibility, but experience adjusting to different incoming shots until you become used to making adjustments and have confidence you can do so.
You don't need to practice against every type of weird incoming shot to be able to deal with each of them. What's needed are two things: command of your shots, and general experience in adjusting. By playing lots of matches against lots of different players (whether practice, league, or tournament) you develop the habit of adjusting. And then, when you do play something different, you don't need to spend huge amounts of time learning to adjust to it; you've already developed that habit. If you have command of your own shots, and have developed the habit of adjusting to different shots, then you'll have little trouble adjusting to whatever an opponent can throw at you. This, and a little tactical thinking to figure out the weakness of the opponent's shots, are all that's needed to give you the advantage.
The key thing to remember is this - if the opponent is doing something weird, then pretty much by definition it's not standard technique, and there's probably a reason for that. If you have command of your shots and are used to adjusting to opponents, and do a little tactical thinking to figure out the weakness of the opponent's technique, then your more standard technique will give you an advantage over this less standard technique.
One hint that'll help against most "weird" rally shots: keep the ball deep on the table, and you'll have more time to react to their shots. Remember that they are used to your more standard shots, while you are not as used to theirs.
Beginners dread playing against "weird" players. Top players look forward to it knowing the player's game is flawed.