Greetings,
I have written on this issue before. The text below is a copy of a previous post of mine. Please notice the change on meanings of English words when they are negative (the difference between must and must not etc.)
http://www.turkishclass.com/forumTitle_6_2058

That's a very good question which could be a topic of a lesson if somebody would have write it.

1. must > zorunda olmak (zorundasın, zorundayım etc)
I must go. > Gitmek zorundayım
You must stay here. > Burada durmak zorundasın.

The negative changes the meaning completely and tells us that something is forbidden.
must not > -me+meli (koşmamalı, gitmemeli, yapmamalı Here -me is the negative while -meli expresses neccessity.
You must not move. > Haraket etmemelisin.

2. have to > a. zorunda olmak b. gerekli olmak
You have to go. >
a. Gitmek zorundasın. (You must go)
b. Gitmen gerekiyor. (You need to go)

I can't find a better translation for have to. So either I translate it as must to or need to when affirmative.

The negative can be build same way.
You don't have to go. >
a. Gitmek zorunda değilsin. (You don't have to go. Obviously this can't be translated with must not and vice versa)
b. Gitmen gerekmiyor. (You don't need to go)

3. need to > gerekli olmak
You need to go. > Gitmen gerekiyor.
I need to go. > Gitmem gerekiyor.

Negative can be build the same way:
You don't need to go. > Gitmen gerekmiyor.
I don't need to go. > Gitmem gerekmiyor.

4. should
Depends on the meaning of English sentence. Has different usages in English thus varies in translation.

You should go. >
a. Gitmelisin (present)
b. Gitsen iyi olur. (present)
c. gitmeliydin (unreal past, now ,its too late to go)

You shouldn't go.
a. gitmemelisin (present)
b. gitmemeliydin. (unreal past: You shouldn't have gone)

Here notice that "gitmeliydin" and "gitmemeliydin" are unreal past expression where it is too late to act correctly now. Normally in English perfect temses would fit better in this situation but I think people tend to use present tense as well. For instance while "You shouldn't have done this" is the correct sentence for unreal past some may use "You shouldn't do this", thus I have included the unreal past meanings of should and shouldn't as and

5. may
I prefer to translate this with possibility expressions and the suffix is -ebil

You may go. > Gidebilirsin/Gidebilirsiniz.
You may sit here. > Burada oturabilirsin/oturabilirsiniz.
She might come. > Gelebilir.

The negative changes the meaning completely as in English "may not" is used like a polite way of "must not" if I understand correctly. Again if I understand correcty "may not" and "might not" have very different usages in English. I have seen "may not" used as warnings in the context of "Not possible to...", while "might not" sound to me more like "Possible not to...".


You may not enter. >
a. İçeri giremezsiniz. (It is not possible for you to enter)
b. İçeri girmeyiniz. (Please don't enter)

She might not come. > Gelmeyebilir. (There is a possibility that she is not going to come.)

You might not come. > Gelmeyebilirsin. (There is a possibility that you are not going to come.)

Notice that I'm using "may not" as the unpossibility to do something and "might not" as the possibility for something not to be done.

6. Shall
Shall we go? Gidelim mi?


All in all this is an advanced issue. I would suggest starting to practice with -meli -malı (nessassity suffixes).
gitmek > git > git+meli > git+meli+yim
to go > go > need to go > I need to go.

gitmeliyim > I need to go.
gitmelisin > You need to go.

But the negative with the netaive suffix -me and -ma (added like, me+meli ma+malı has a different meaning.

gitmemeliyim > I must not go.
gitmemelisin > You must not go.

The biggest problem is that, in comparizon, not every version is the same. When I listen to Turks talking, they use those forms as they want to and every time as it is written in grammar...
so zorunda olmak means have to but also must, but gerek has the same meaning... is one of them stronger?

"zorunda olmak" is the strongest. Above I have translated must with only "zorunda olmak".

must < > zorunda olmak

have to < > a. zorunda olmak b. gerekli olmak

need to < > gerekli olmak

"zorunda kalmak" is different than "zorunda olmak" because it expresses unwillingness. When you say "zorunda kaldım" you mean that there was no other choice so you had to do something.

Erdinc! Thank you very much!