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Lustig vs. witzig vs. komisch

The German words lustig, witzig, and komisch can all be translated as funny, but they are not always interchangeable. Lustig is the most general term for something amusing, witzig implies cleverness and wit, while komisch has a dual meaning of both comical and strange or odd.

Lustig

A1
This is the most common and general word for funny. It describes something that is amusing, lighthearted, and makes you laugh in a cheerful way. It can also simply mean fun.
Der Film, den wir gestern gesehen haben, war sehr lustig.
(The movie we watched yesterday was very funny.)
Mein Onkel ist ein sehr lustiger Mensch, er lacht immer.
(My uncle is a very cheerful person, he is always laughing.)
Es war eine lustige Party mit guter Musik und netten Leuten.
(It was a fun party with good music and nice people.)
Die Kinder haben sich ein lustiges Spiel ausgedacht.
(The children invented a fun game.)
Das kleine Kätzchen, das dem Wollknäuel nachjagt, sieht lustig aus.
(The little kitten chasing the ball of yarn looks funny.)

Witzig

B1
This word is derived from der Witz (the joke). It describes something that is witty or cleverly funny. It often refers to intellectual humor, a smart remark, a pun, or a well-constructed joke with a punchline.
Deine witzige Bemerkung über die Situation hat alle zum Lachen gebracht.
(Your witty remark about the situation made everyone laugh.)
Sie ist bekannt für ihre witzige und schlagfertige Art.
(She is known for her witty and quick-witted manner.)
Das Ende des Buches hatte eine wirklich witzige Pointe.
(The end of the book had a really witty punchline.)
Die Karikatur in der Zeitung war sehr witzig und treffend.
(The caricature in the newspaper was very witty and accurate.)

Komisch

A2
This word is ambiguous and its meaning depends heavily on context. It can mean funny in a comical, slapstick, or theatrical sense. However, it is more frequently used to mean strange, odd, weird, or peculiar.
Der Clown im Zirkus machte ein komisches Gesicht.
(The clown in the circus made a comical face. (Meaning: funny))
Er hat einen sehr komischen Gang, es sieht übertrieben aus.
(He has a very comical walk, it looks exaggerated. (Meaning: funny))
Ich habe ein komisches Gefühl bei dieser Sache.
(I have a strange feeling about this matter. (Meaning: strange))
Die Milch schmeckt komisch, ich glaube, sie ist nicht mehr gut.
(The milk tastes funny/strange, I think it has gone bad. (Meaning: strange))
Er verhält sich seit gestern sehr komisch.
(He has been behaving very oddly since yesterday. (Meaning: strange))
Hast du auch dieses komische Geräusch aus dem Keller gehört?
(Did you also hear that weird noise from the basement? (Meaning: strange))

Summary

In short: Use lustig for general, lighthearted fun and amusement. Use witzig for clever, intellectual humor and witty remarks. Be careful with komisch; use it for comical, slapstick-style humor, but be aware that it more commonly means strange or odd. Context is crucial for understanding komisch.