I have dual citizenship of Japan and Iran, and I'm studying in the U.S. for the past six years through F-1 visa. I've lived in Japan for the first 15 years of my life, and I've never visited Iran. Since Japan doesn't recognize dual citizenship status, I needed to renounce Iranian citizenship, which I obtained by birth from my father of Iranian origin and is almost impossible to renounce. However, Japan recognizes renouncement of foreign citizenship just through a short paperwork, which is processed only within Japanese legal system. However, this renouncement system is local and not necessarily considered valid oversea. Does the U.S. have a similar system? If not, does this Japanese system of renouncement of citizenship have any effect in the U.S.?
We do not have a law requiring you to renounce citizenships that you might hold, like the Nationality Law. I am not sure what you mean saying that renouncement is processed only within the Japanese legal system -- that is how it is everywhere, and there is no international authority or clearing house that handles citizenship renunciations. The effect of renouncing Japanese citizenship would be that you are then no longer a citizen of Japan: I can't find an explicit law prohibiting an exclusively-Japanese citizen from renouncing his citizenship and becoming stateless. A dual citizen would then be exclusively a citizen if "the other country", thus you would become strictly an Iranian citizen.
According to the Civil Code of Iran you would be an Iranian citizen under clause 2 of Article 976. Article 977 allows accept a different citizenship but that would not apply if you have an Iranian father (and I guess does not actually get rid of your Iranian citizenship). Article 988 sets conditions for Iranians to abandon their nationality: you must be 25 or older, have renounced all property rights in Iran by transfer to Iranian nationals, have done your military service, and, have approval of the Council of Ministers. So yeah, not possible.
Article 14 of the Japanese Nationality Law requires you to "choose either of the nationalities" before reaching 22, and furthermore
Choice of Japanese nationality shall be made either by depriving himself or herself of the foreign nationality or by the declaration provided for in the Family Registration Law in which he or she swears that he or she chooses to be a Japanese national and that he or she renounces the foreign nationality (hereinafter referred to as “declaration of choice ”)
Article 16 says "A Japanese national who has made the declaration of choice shall endeavour to deprive himself or herself of the foreign nationality".
The bold part above seems to resolve that paradox, although that is based on a US-style interpretation of law and working from a translation of the law. That is, the requirement is that you try, not that you succeed (which is impossible in the case of a person with an Iranian father).
There would be an effect in the US. If you renounce Japanese citizenship, you're strictly an Iranian national, and that has one consequence. What is not clear is whether the US recognizes, in any way, a renunciation which Iran doesn't recognize. This case features a person with renounced Iranian citizenship (he is also a US citizen), who was approved for a security clearance based in part on his renounciation. This gives some indication that the US does not care that Iran makes renunciation next to impossible.
This is of course just for informational purposes and calls for an immigration attorney if it really matters.