to suck
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to suck on
To move something around in the mouth and work it with the tongue and lips in order to take in its flavor or dissolve it, without biting it.
Das Kind lutscht genüsslich an einem Bonbon.
The child is happily sucking on a piece of candy.
The three meanings are clearly separated by context. The neutral meaning refers to edible things, the colloquial one to a bad situation, and the vulgar one to a sexual act.
Ich könnte stundenlang an diesem Eis lutschen.
I could suck on this ice cream for hours.
In the basic meaning, the verb is used either with an accusative object or with the preposition 'an' + dative. 'An' is used when you are only sucking on the surface of something.
Das Baby lutscht zufrieden an seinem Daumen.
The baby is contentedly sucking on its thumb.
The meaning 'to be very bad' is a direct borrowing from American English ('to suck'). It belongs to youth slang and is very informal.
Ich finde, der neue Film lutscht total.
I think the new film totally sucks.
In the sexual meaning, 'lutschen' is a colloquial expression and is often perceived as vulgar. It should be used with great caution, as it can quickly come across as offensive.
Er wurde wegen seiner vulgären Sprache kritisiert.
He was criticized for his vulgar language.
to annoy
'nerven' and 'lutschen' can sound similar in very colloquial language when something is bad or annoying. 'nerven' is the normal and clearly more neutral word for this. You can use it in many everyday situations. In this use, 'lutschen' means roughly that something is very bad or annoying, but it sounds very slangy and can also come across as crude. That is why it fits better among friends or in youth slang, not in polite or official situations.
Der neue Stundenplan lutscht, weil wir jeden Tag sehr spät Schluss haben.
The new schedule sucks because we finish very late every day.
Mich nervt es, wenn der Bus jeden Morgen zu spät kommt.
It annoys me when the bus is late every morning.