"I have to finish my work."
Translation:Jag måste avsluta mitt arbete.
Sluta means 'to quit, to stop'. If you say "Jag måste sluta med projektet", you mean that YOU have to stop with the project, but that doesn't mean the project is over.
Avsluta means 'to finish. to terminate'. If you say, for example, that "Jag måste avsluta projektet" it can mean either that you have to finish the project or that you have to terminate it. Either way, it has to come to an end.
Slutföra means 'to finish [and get it done]'. If you say "Jag måste slutföra projektet", you mean that you have to finish the project as you set out to do, not quitting or terminating it until it's done.
Does that help to explain the differences?
So sluta is like stopping temporarily, while avsluta means stopping forever, and slutföra means stoping something once it has come to an end?
For example, if you temporarily stopped watching a movie to get a drink, you would say sluta, but if you stopped watching the movie midway because you didn't like it, you would say avsluta, and finally,if you stopped watching the movie because it is over, it would be slutföra (but it could also be avsluta). Is this all right?
Late answer (I don't know if you still need it, I'm not Swedish but it's my way to remember the difference)
Slutföra is based on two words slut (to end) and föra (to bring, to conduct). So you bring the project to the end of it, if it begins at A it will end at Z (for the Swedish at Ö), it is entirely done, 100% of the project.
For avsluta, it is more like the project is stopped after 75% for whatever reasons, it's over but not finished! Someone puts a stop at it.
I get frustrated when you hover over a word (for the first time it is introduced) and it gives a definition (in this case, the definition for slutar: stop, quit or finish...and then when I used finish in the answer it says it's incorrect. Reading below helps - but it's kind of conflicting. This is not the first time I've found this. Why ?