
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.

to disgust
To find something or a situation extremely repulsive or unbearable. Often used in the expression 'Das kotzt mich an' (That disgusts me / That really pisses me off).
Diese ständige Ungerechtigkeit auf der Welt kotzt mich einfach nur an.
This constant injustice in the world just absolutely disgusts me.

to vent
To give free verbal rein to one's anger, frustration, or resentment; to complain intensely about something or someone.
Nach der Arbeit hat er sich bei einem Freund erst mal richtig über seinen Chef ausgekotzt.
After work, he first really vented to a friend about his boss.
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
Both words refer to expelling stomach contents. Sich übergeben is the neutral, usual form and also works in factual situations; kotzen is much more colloquial and cruder. In a conversation among friends, kotzen may be appropriate, while in a report or at the doctor’s, sich übergeben is more suitable.

Nach dem verdorbenen Essen musste Jonas kotzen.
After eating the spoiled food, Jonas had to puke.
Nach dem verdorbenen Essen musste sich Jonas übergeben.
After eating the spoiled food, Jonas had to vomit.