Do these men call themselves "princes of Romania" because they are the only males close to the throne who are Hohenzollern? Being that HM has no sons, I am guessing they are assuming the head of the house is officially there's upon his passing?
I am guess also that these men do not realize nor do they respect HM decree that allowed women succession rights and gave Nicolae the title HRH, prince of Romania?
I do have a question regarding Elisabeta-Karina... Is she in line for the throne? I notice that she was not given the title HRH, Princess of Romania, and does not go by that or is addressed by such... Can someone explain why she was not included in the decree that gave Nicolae a title and succession rights?
Is she not a princess?
I believe the argument here isn't so much that they believe they're the heirs to Michael, but rather that they believe they're the rightful heirs to Carol II.
Carol had two sons, Carol Lambrino and Michael I. Carol Jr was born from Carol Sr's first marriage, which was later annulled, while Michael was born from Carol Sr's second marriage. As such, Carol Jr is older than Michael. However, his legitimacy wasn't established until 1955 (in Portugal and 1995 in Romania) - after Michael had already been established as king. Carol Jr never claimed to be the rightful heir of Carol Sr, but his son, Paul, has claimed as much.
Basically, Paul's claim is that because his father was born first, and legitimately as confirmed by the courts of Romania, and he himself is the eldest son of his father, then he is the head of the house and the rightful claimant to the throne. However, in a way Michael's claim is stronger - when Carol Sr abdicated in 1925 it was in favour of his younger son, Michael, establishing him as the heir. Then, when Carol Sr was overthrown in 1940 it was Michael who was put on the throne and crowned. Thus, Michael ruled (in as much as he ruled at all) by conquest, nullifying the actual order of succession. As such, Paul's claim to the Romanian throne becomes rather similar to Charles Stuart's claim to the British throne in the 18th century - yes, he has the better claim in terms of primogeniture, but the ruling party (in as much as there is one) does so by right of conquest, nullifying the better claim.
This is going to become even more of a problem when Michael dies, as he doesn't have a male heir and the Romanian throne requires a male heir. While he can say that he's changed the rules of succession to allow for inheritance by his daughter all he wants, it's not entirely supported legally (owing to the lack of a throne). He might have been better of naming his grandson as his heir, but even then there's still the issue of Paul and his legitimate, male-line descent.