Translation of Russian Terms
(First) degree is usually the most appropriate translation, since a Russian диплом is awarded after five years' specialised study at an institution of higher education. The use of diploma implies a shorter course, or one of a lower academic standard.
First should be included only when it is necessary to distinguish this degree (=диплом) from a higher degree (ученая степень).
I've only got a first degree.
Дипломная работа is difficult to translate into English, because there is nothing of this kind in most higher educational establishments in England. In order to graduate, students only have to pass the necessary examinations. In some institutions, however, mainly newer ones, students also have to write a dissertation, that is, a sort of extended essay based on some independent study or investigation, and this practice seems to be spreading. Dissertation could therefore be used as a translation of дипломная работа, bearing in mind that it exists only in some English institutions. The SOED (Shorter Oxford English Dictionary) defines dissertation as "a discourse, a spoken or written treatment of a subject at length". In American English, however, dissertation is a work submitted for a higher degree (BrE thesis). This fact, and the possible confusion with the Russian диссертация, make dissertation a far from ideal translation of дипломная работа.
The only other solution seems to be some descriptive expression with graduation, for example, graduation essay/ paper/dissertation.
Дипломный пpоект can be translated as graduation project. Remember, however, that this is not a set expression and that project has a wider use in modern English.
Зaщита дипломной работы/дипломного проекта
Even in those institutions where students write a dissertation there is no occasion corresponding to the Russian защита. The dissertation is simply marked by the examiner(s) together with the student's examination papers.
One possibility is to use the expression oral (examination) or viva, as in the case of theses but this has various disadvantages. Firstly, an oral examination (or viva) is not conducted like a защита. Secondly, it is not clear how to specify the idea of a first degree. Graduation/final oral(examination) or viva is possible, but this does not suggest the discussion of a dissertation or paper. Moreover, it would be better to keep the expression graduation/final oral (examination) as a translation of the oral part of the государственный экзамен.
In view of all these complications, there seems to be no good alternative to the literal translation defense of one's dissertation or graduation paper/project. Remember, however, that this will not be clear to English people without an explanation.
Graduate (from a university/college) can generally be used as a translation in formal or semi-formal style. In non-formal style, however, some other version is more appropriate, for example, to take one's degree.
In cases where the fact of having passed the examinations, etc. is not the central idea, English people often use the verb to be with at, or to go with to.