BIG FLAW IN ANGEL BEATS STORY LINE

There are quite a few theories on this. One is that, because Otonashi donated more organs than just his heart, he couldn't go to the afterlife until all of the people who recieved his organs died (because they were still tethering him to the real world). That explains the 'long time' statement, because their bodies might not have rejected his organs and they could have lived for quite a while.

Another idea is that Otonashi didn't belong in the afterlife, so he was wandering in Purgatory for a long time. He couldn't go to the afterlife, because his life had been fufilled (he accepted Hatsune's death and all he wanted to do was help people, which he did). He couldn't reincarnate, because Kanade needed to thank him so that she could move on, and if he reincarnated then he wouldnt be himself for Kanade to thank. He eventually got pulled to the afterlife because Kanade's will to thank him increased even more. It could have also helped to bend the rules because Otonashi's wish was to help people directly, but his donations were indirect.

It really depends on your personal interpretation, because it was left unmentioned in the anime.

In Shinto belief, there is nothing such as time in afterlife.

Time in that world is not the same as her. Like there is no time for god, i guess? So time there is let`s say in one pleace and here on earth in a another.

ChorusRomance's second theory is a bit correct. If you payed attention to the dialogue, you should know that Otonashi's soul wandered a long time after his death because he "may" have had amnesia right at the moment of his death. There was no indication whatsoever that he did have amnesia, but the thing is, he donated his organs before he died and because of that his purpose in his world was fulfilled which gives him no reason at all to go to Kanade's world. So it's either his soul did forget of his last actions, or it's just a matter of fate and luck.