Weightlifters are what you see every 4 years at the Olympics and it's been around since the early 1900's it's composed of 2 events one is the snatch a power movement from the floor to over head and the clean and jerk where you pull the weight from the floor to the top of your chest and the jerk the weight above your head. You get 3 lifts of each and your biggest lift counts. This used to be a clean and press event was changed in the 1970's because of judging the technique of the press was difficult. This is split into different weight categories and it's a very technical and powerful sport and takes years to master. Unlike the other 2 sports your not allowed any supportive gear other than a belt, knee sleeves and wrist wraps.
Powerlifting is compiled of 3 different lifts, the squat, deadlift and bench press. This is also where you have 3 lifts per lift and your biggest lift counts. This is newer than weightlifting and has been around since the 1950's. Undeniably this is also very technical and in my opinion maybe a bit more than weightlifting. This is purely about power and strength in static lifting positions. Powerlifting also has weight class decisions but you are allowed to wear supportive suits which ultimately gives you the advantage of being able to lift more weight as your externally supported. Also, unlike strongman you are not allowed to wear wrist wraps/straps which allow you to deadlift the weight without having to worry about your grip.The allowance of supportive suits is the best part of powerlifting as you can see the physical limits you can push a body to.
Strongman started in 1977 at Universal Studios in California, so this is the newest of the 3. This is a sport I love so there undoubtably bias towards it. It's a combination strength, power, speed and endurance. There are about 30 different standard events that are used mostly and maybe another 20-30 events that certain competitions create. Within all these events there are numerous variations with in it E.G. The size of the log, where the weight is distributed on the yoke or farmers, size of the handles, type of bar, diameter of dumbbell, etc. So of all I personally feel this is the hardest to train for as you have to be physically fit to tolerate the endurance of the competition and at the same time need the strength and power on all events. On average there are either 5 or 6 events and this can be done in one day or 2. You only get one chance at an event with a trial pre event. There are 3 weight divisions of under 90kg, under 105kg and open (which is anyone over 105kg. In the UK there isn't a formal governing body that sets the guidelines like the IPF do in powerlifting and the IWF in weightlifting but as the sport growing it's getting more organised. In the USA they have NAS which is the only one I know of that is widely known.