I am currently holding a PhD studentship at a good university, but I think that what I have been offered is different to what I expected. I am really interested in the reseacrh, but think it is more structural than structure based design. I need to speak to my supervisor to find out, but if this is the case and I do not want to pursue that area of research, is it okay to turn around and decline the offer after already accepting it?

You can turn down an offer of a PhD after accepting it. It won't make you very popular, but if your supervisor understands your reasons he shouldn't be too annoyed. You should let him or her know of your decision as soon as possible so that they have time to recruit a new student (in some cases they may loose the studentship, if they haven't got a candidate in time).

You should also be sure that turning it down is the right thing to do, if you really want to do a PhD then you may not be able to find a new place before October.

I'm in a similar situation and unsure what to do. I recently had an interview for a PhD studentship and one of the supervisors promised the department would reimburse my travel expenses, amounting to £250 as the interview was a short airjourney away. To my surprise, I was offered the studentship almost on the spot. However, I'm waiting to hear back from another, potentially better project. Can the department ask me to pay back the reimbursed expenses, if I turn down their offer?

They shouldn't ask for your interview expenses back - especially if they were offered before you came for interview. Make sure you inform them as quickly as possible when you've made you decision.