Can anyone perhaps tell me how I could get a summer job in Marmaris?

What you could do is to find out through a site of a travel agency to what hotels many people of your country are going. Then, if you have the hotel names, find their sites and send them a mail asking if they need staff. That's how many Dutch girls find a summer job. I know some restaurants who want new staff but you need to speak Dutch...

But it's illegal unless you get a work permit.

Yes they might do that. Some tourists expect to get serviced in their own language with food from their own country so it's popular for theme restaurants to hire natives. But many restaurants don't want to bother going through with all of the paperwork, they want to pay their staff the lowest pay possible and be able to kick them out without notice.

Anonyoo > what kind of job did you have in mind? I'd advice you to check out the place because many are just trying to take advantage of their staff. Be sure to have cash enough for a plane ticket if you don't like it.