How do I say that I'm Russian?
The official Chinese translation for "Россия" (Russia) is 俄罗斯.

The full name of Russia is "Российская Федерация" (Russian Federation), and the official Chinese translation is 俄罗斯联邦.

From the year 1721 to 1917, the dynasty of Russia was called "Российская империя" (Russian Empire), and the official Chinese translation for that dynasty is 俄罗斯帝国, or 俄国 for short.

As a result, don't use 俄国 unless you really mean the Russian Empire from the year 1721 to 1917.

Russian = the person of Russia = 俄罗斯人

Therefore, "I am Russian" should be "我是俄罗斯人".