Does it work?
No.
Laxatives work too late in the process of digestion to make a difference. They only have an effect on the food out of which all nutrients (and fats and calories!) have already been absorbed. It's just too late to make a difference. If the scale indicates a lower weight, that's from dehydration and because your bowels are empty. There are severe side effects to using laxatives, however.
Diuretics dehydrate you. They don't get rid of any fat or food, the only reason the scale might indicate a lower weight, is because there are fewer fluids in your body. There are also serious side effects to the use of diuretics.
When you throw up after you eat, you can't get all of the food out. No matter how good you think you are at throwing up, some percentage of the food will stay in your stomach. And even though you could say throwing up has more of an effect on your weight than diuretics or laxatives, because there's just less food for your digestive system to work with, there are so many adverse side effects that saying 'it works' wouldn't be right. Not if you consider the fact that it could kill you.

Adverse effects
Continued laxative use can have severe physical consequences and side effects. These are: flatulence, bloating from the water your body starts to retain, dizziness, headaches, nausea, vomiting, severe abdominal pain, constipation, (bloody) diarrhea and permanent damage to your bowels, dehydration that could lead to kidney damage, renal problems, impaired vitamin absorption, chemical imbalances in your blood, muscle weakness and paralysis, electrolyte imbalances leading to irregular heartbeat or heart attack, and even (sudden) death. The more and the longer you use laxatives, the worse the side effects will be. And these side effects don't just happen to some of the people that use them, but to all of them, eventually. Yes, that includes you.
Diuretics use also does serious damage to your body, in much the same way as using laxatives. It can cause bloating from the water your body starts to retain, dizziness, headaches, dehydration that could lead to kidney damage, increased levels of uric acid in your blood, muscle weakness and paralysis, electrolyte imbalances leading to irregular heartbeat or heart attack, and even (sudden) death. And just as with laxatives: the more and the longer you use them, the worse the side effects will be.
Throwing up has even worse and more rapid consequences for your body. It can cause bloating, swelling of the feet and ankles, weakness, fatigue, dizziness, fainting, dehydration, choking, enamel erosion leading to cavities and tooth decay, swelling of the salivary gland, tearing of tissue in the mouth and throat, pain with swallowing because of inflammation of the esophagus, spontaneous regurgitation of food, numbness and tingling in the limbs, abdominal pain and chest pain due to peptic ulcers, stomach rupture, vomiting blood, rupture of the esophagus (can be fatal), irregular of abnormally slow heart rate, heart failure, and even (sudden) death. The longer you go on inducing vomiting, the worse the damage to your body will be.

How to stop
Using laxatives or diuretics and throwing up is addictive.
With laxatives and diuretics there are physical withdrawal symptoms. With all three there is a psychological addiction, a feeling of control or safety, the habit of doing it. This is why it's not easy to give it up, to stop doing it.
It's very important that you do, however. Especially since using laxatives and diuretics does not help you lose weight anyway, and since all three methods are very hazardous to your health and could kill you.

If you're taking laxatives, the easiest way to stop taking them is to go 'cold turkey'. Flush all that you have left through the toilet and don't buy new. Yes it's hard. You will experience withdrawal symptoms, like abdominal pain, bloating, mood swings, nausea and fatigue. Your body has become dependent on the laxatives, leading to constipation. This will pass, however, usually within two weeks your body will have gotten back to normal. In the mean time keep reminding yourself why you're not using it anymore: because it will destroy your body and it doesn't work at all anyway.
Diuretics are a different story. If you suddenly stop taking diuretics, you will be faced with edema. You should slowly cut back and if at all possible, seek medical assistance to minimize risk.
If you throw up after you eat, stop doing that right away. The sooner you stop, the better your chances to minimize damage to your body. If you do throw up, don't brush your teeth right after. Drink water, that is better for your teeth at least.