My understanding of the Ikko Ikki (or Ikho Ikki - there seems to be some conjecture about the anglicised spelling) is that not only did they control a province in Japan, but they also had temples scattered around the country. I understand that they practiced a very specific type of Buddhism, and that they were monks first and foremost. However, I am struggling to find good sources that talk about their martial capabilities. They had some level of organization and real capabilities - how else would they hold off the Oda for so long - but I don't know exactly how they managed it. How did the Ikko Ikki function martially, and how were their troops trained? What kind of martial arts were practiced, if any?
I do not believe there's any evidence that the Ikko Ikki had any special training or organization. They might have had a higher morale due to religious zeal, but that's conjecture. Negoro temple, who responded to Honganji's call to resist Oda Nobunaga, and Suzuki's mercenaries did have a lot of guns, thanks to their well-established position as gun merchants and mercenaries. But while they set the Oda back tactically a couple of times, they weren't really the reason Ishiyama Honganji held out for so long.
There are four reasons Ishiyama Honganji held out for so long.
Also, after Honganji surrendered, Nobunaga fired Sakuma Nobumori (one of Nobunaga's longest-serving retainers) for (among other reasons) sitting on his ass and doing nothing during the last few years when he was in charge of the siege. Whether or not this firing was reasonable, Nobunaga certainly thought Nobumori was not fighting, negotiating, or trying any subterfuge or stratagem against Honganji. So that might be a factor as well.