Points of correction here, because there's a lot of misinformation going around, and because this is a topic where people get these things wrong VERY frequently in the non-native Japanese-speaking parts of manga fandoms.
1. Pronouns in Japanese are a matter of social status and the level of formality implicit to the circumstances. Gender is a concern only loosely connected to pronouns, but I'll touch on this point later.
2. "Ore" and "boku" are pronouns used in fairly particular circumstances. To refer to oneself as "ore" is to be especially arrogant, as there really isn't a situation where the level of formality is low enough to put it in an acceptable zone of politeness. The only time someone can get away with using "ore" is in a circle of companions who are more or less on the same level (i.e. all can use "ore" around each other); anytime else, it's inexcusably rude. "Boku" is far more innocent in tone, but is strongly connected to an age range; polite young boys (younger than about 16; the cutoff age is no later than the day you start high school) may refer to themselves as such. This being a convention specific to boys isn't a rock-solid thing; it's technically gender neutral. However, relatives or close friends of the family may refer to a young boy as "boku" in the third-person, despite it usually being a first-person pronoun, as a way to tease them about their young age (or, putting the boys "in their place", depending on your lens). Girls tend to begin to develop socially mature personae at a younger age than boys, which lead to girls imitating this teasing third-person use of "boku" towards boys of their own age group. Enough repetitions made this a social convention, giving the vacuous impression that "boku" is a masculine pronoun. This is incorrect; rather than "boku" being "masculine", it's better to say that "boku" is a "non-feminine" pronoun.
In recent decades "boku" and later even "ore" started to become adopted for use by tomboyish female characters in media - "boku-kko" and "ore-kko", respectively. This is because these characters are attempting to set themselves apart from modern Japanese feminine norms. Boku-kko do so in a fairly mild manner, but this is nevertheless a rejection of the most accessible female aspects and circles, to at least some degree. A boku-kko typically will have few female friends. (Watch Kino no Tabi for an example of one; another recent standout is Idolmaster's Yumemi Riamu, who does so because - despite having a very feminine image and not being particularly masculine in any way - she is poorly socially-adjusted, can't relate well to other women, and is largely bad at adjusting her speech patterns to the level of social formality when the heat is on.) Ore-kko are more intense in this respect, because for a girl to use an arrogant pronoun like "ore" - which isn't even socially acceptable for casual use by men - is her signaling that she is fully disregarding other people's opinions. Doing so is an enormous faux pas in Japanese society, and is the mark of social delinquency 100% of the time; if an ore-kko has any female friends at all, they're almost guaranteed to be other delinquent type characters.
3. "Watashi" is the default socially-neutral pronoun for both men and women in Japan. Women will, more often than not, shorten this to "atashi" at all levels of formality lower than business-polite keigo; doing this is not construed as speaking informally. "Watakushi" is more formal and more bold than "watashi", but is never used by men except when attempting to put on an effeminate air. Only the prim-and-proper daughters of wealth (the "ojou" archetype, named because these characters are often depicted as having servants or bodyguards who refer to them with the third-person "ojou-sama" pronoun) will actually use "watakushi" outside of business meetings, for this reason.
In effect, this does mean that girls and women get to use distinctly feminine pronouns without fear, whereas for a boy or man to do so is to put his social status at risk.
4. "Washi" is a pronoun for old people of either gender, full stop; men, women, doesn't matter, if they're old then that's that. The only pronoun for use by old men ONLY is "wagahai", which is theatrical to the point of buffoonery. Case in point: Bowser from Super Mario Bros. uses the "wagahai" pronoun in his Japanese lines, and he is most definitely stuck squarely in the buffoon's role despite being the designated villain of the series.
5. "Akakushi" isn't a thing. Nobody says that at all.
6. "Jibun" is not even, strictly speaking, a regular pronoun; it translates to (depending on the subject being discussed) some variation of "self": "myself", "themselves", or even "itself". "Jibun" can and frequently is used to refer to inanimate objects, rather than people. The only exception to this is found in the Okinawa dialect (borrowing the use of Idolmaster characters, Ganaha Hibiki - an Okinawan girl - uses "jibun" as a pronoun; this serves no purpose in defining her personality besides placing her origin squarely in the southern islands). The use of "jibun" as a pronoun by soldiers is a convention of the soldier debasing himself utterly in the presence of a commanding officer; think of it as them saying "Sir! I am not a living being, Sir! Please mold me in your image, Sir!" This use of "jibun" has fallen into disuse due to the JSDF's ongoing attempt to clean up their image compared to a century ago, and it's no longer appropriate for people in military service to dehumanize themselves.