kotzen
to puke
To vomit; to expel stomach contents through the mouth. This word is colloquial.
Nach dem verdorbenen Essen musste er die ganze Nacht kotzen.
After the spoiled food, he had to puke all night.

to puke
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to puke
To vomit; to expel stomach contents through the mouth. This word is colloquial.
Nach dem verdorbenen Essen musste er die ganze Nacht kotzen.
After the spoiled food, he had to puke all night.

The verb 'kotzen' (to puke) and its variants are very colloquial. It is used in informal conversations or in situations where strong negative emotions are being expressed.
Mir ist total schlecht, ich glaube, ich muss gleich kotzen.
I feel really sick; I think I'm about to puke.
The three meanings can be recognized well from the sentence structure. The literal meaning often stands on its own. The expression 'etwas kotzt mich an' shows strong disgust or annoyance. The reflexive form 'sich auskotzen' means to complain or vent.
Ihm war so schlecht, dass er kotzen musste.
He felt so sick that he had to puke.
In the figurative meaning, 'kotzen' is almost always used in the fixed expression 'etwas kotzt jemanden an'. The thing that is annoying is the subject of the sentence, and the person it bothers is in the accusative.
Die ständige Lügerei in der Politik kotzt mich an.
The constant lying in politics really disgusts me.
The expression 'sich auskotzen' is reflexive and means to let off steam. The prefix 'aus-' is separable. It is often supplemented with the preposition 'über' (+ accusative) to say what someone is complaining about.
Er musste sich mal richtig über die Arbeit auskotzen.
He really needed to vent about work.
to hand over / to vomit
'sich übergeben' and 'kotzen' both mean that someone vomits. The most important difference is style. 'sich übergeben' is more neutral and fits better at the doctor’s office, at school, at work, or in polite conversations. 'kotzen' is colloquial and much more direct. You are more likely to hear it among friends or when someone is speaking roughly. In a formal or medical situation, you should use 'sich übergeben'. 'kotzen' can quickly sound impolite or too strong.

Im Bus wurde Max schlecht, und kurz danach musste er kotzen.
Max felt sick on the bus, and shortly afterward he had to puke.
Nach dem Essen musste sich Lisa mehrmals übergeben.
After the meal, Lisa had to vomit several times.