When will I become an EU citizen?

I am getting married next April to a British guy. Been in the country on a work permit for 18 months already.
After I get IDL does that make me an EU citizen?
I ask because we want to move to Greece, and EU citizens are allowed to work there without a permit as far as I know.
Thanks

Your marry your British guy.

23 months after you get your Further/Limited Leave to Remain after marrying him, then you apply for Indefinite Leave to Remain.

Once you have Indefinite Leave to Remain AND have lived in the UK for 3 years AND haven't been out of the UK for more than 270 days in those 3 years, no more than 90 days in the last year, then you can apply for BRITISH citizenship.  You will not be applying for EU citizenship.

However, holding British citizenship AND a British passport means that you can travel and live and work within the EU as any other British citizen could.

Do you think its quicker to apply for leave to remain from my work permit rather than from my marriage?  by the time i am married i will only have 18 months left.....can i apply for citizenship then or do i have to apply for LTR and then wait and then apply for IDR

You can apply for Indefinite Leave based on your work permit after 4 years (actually, 3 years 23 months!).  Then you have to hold Indefinite Leave for 1 year before you can apply for citizenship.

Theres no way to become a citizen sooner?
Can I apply for indefinite leave by trying to get an unmarried partner visa?

You and your partner will have to show 2 years cohabitation.  Then the Unmarried Partner visa is for another 2 years.  And then you apply for Indefinite Leave.  And I think with Unmarried Partner (at least how it stands now), that's an "other" situation.  Which means living here 4 years and having Indefinite Leave for 1 year prior to application.  It's only through *marriage* that you wait 3 years - any other reason it's 5, really.