According to numbers I read, about 33% percent of the world population is Christian and about 22% is Muslim. Why have these religions managed to displace traditional religion all over the place?
It can't just be due to political intimidation. Certainly that happened, such as forced conversions on pain of death or slavery. But during the Japanese Empire, there was a similar enforcement of Japanification in conquered areas. Similarly, Indonesia was not even conquered by Muslim armies, but many converted of their own accord.
Christianity and Islam are even still spreading today. The Catholic Church has an increasing presence in East Asia, so much so that it seems that the Chinese government feels threatened and has been taking action. The Pope even just visited South Korea.
Why have Christianity and Islam been so successful when other religions, which have been around for a long time have not spread so effectively? Examples include Zoroastrianism (which Islam seems to have effectively displaced), Judaism, Yazidi, Sikhism, and traditional religions all over the world.
So one of the more interesting essays I've read that touches on this issue (which also notes from the start that it's not a very popular type of question) is called "Muhammad and Jenghiz Khan Compared: The Religious Factor in World Empire Building" by Anatoly Khazanov.
One of the points it raises is why, given that the Arab conquests and the Mongol conquests seem similar in so many ways that large portions of Asia don't practice the Yasa of Genghis Khan, or speak some Turko-Mongol language. In answer to this he notes that although the religion of the mongols tended towards something like monotheism it "lacked any universal moral and ethical appeal." Lacking that "this religion did not promise subjugated peoples anything more than a legitimation of their subjugation."
This is contrasted with Islam. "Even if those who think that originally the Qu'ran was addressed only to the Arabs are right (Sourdel 1983:30), it contained a universal message to the whole of mankind and therefore from the outset had a potential for an eventual integration of the victors with the defeated. It had, or developed, a concept of umma, a supratribal and supraethnic community of believers from which no one could be excluded for ethnic or social reasons and into which people are incorporated on the basis of their religious affiliation."
The whole essay is pretty interesting, you can read it here: http://www.kobiljski.org/CUNY_GC_Spring_2010_Islamic_History/the%20conquests/Muhammad%20and%20Jenghiz%20Khan%20Compared.pdf
I'm not sure that's entirely satisfying to your question but the basic point stands that in contrast to the other available religions Islam and Christianity provided 1. a universal message for all peoples that was 2. easily adapted to the enterprises of the state and 3. was actively proselytized.
It sounds simple but from what I've read, anthropologically speaking, these features are unusual.
I'd like to ask a sub-question: Why did the advent of christianity cause the near-extinction of paganism?