"Kegare" is actually a Shinto concept, not Buddhism.
It literally means "filth" but it is actually a broad term encompassing everything from curses to bad luck to ill fortune. (If you don't know the difference, "ill fortune" is death, "bad luck" made you have the accident that caused it and a "curse" is the spiritual residue of the dead man that will become the cause of further bad luck to others.) The common theme among all "kegare" is that it can rub off on you.
"Onryou" is a Buddhist term but a more traditional word for it is "tatari" which is a Shinto term. You might say that "onryou" and "onnen" are Buddhist translations of Shinto ideas like "tatari" and "kegare".
These concepts do not exist in Chinese or Indian Buddhism.
Worship of "kotodama" and obscession with "wa" is one of the things that hinder open debate and free discussion in Japan.
These concepts are very important in understanding Japan, but they are very difficult for even a native Japanese to grasp fully. Let alone explain to foreigners.
One of the things that we Japanese seldom realize is that our obscession with "wa" is actually a kind of religion and not really a profound respect for harmony. Taking a step out of your own country, you will see that it is rather strange seen from a foreigner's point of view when a Japanese man tells them to "Please understand that we have a deep respect for wa" in the middle of a trade dispute or some such serious conflict. A Westerner (regardless of how he may respond verbally) might think "Why do I have to understand that? You may want harmony, but I don't. I want to win!"
This is how a lot of Japanese-American discussions hit the rocks. The Japanese asks for "understanding" and the American doesn't get why he needs to "understand" some guy he is in conflict with. Especially why he needs to "understand" his opponent's "respect for harmony". "Understanding" is a sissy's word in America and it is usually used when you want to bullshit a dumb broad into bed (as in "Nobody understands me.").
The problem here is that we do not understand ourselves. We in Japan do not "respect harmony" in the Western sense. We worship "wa". Therefore, when we say to Westerners "Please understand that we respect wa", what we are really saying is "WA is our God and you are an infidel."
That may not be an exact translation (owing to the fact that we ourselves are not sure what we really mean) but it is the closest we can get to the spirit of the dismay we feel when we say it. Also it discribes the situation best.
People in Japan are often at a loss why it is so difficult for the Western mind to grasp what we are trying to convey. One of the reasons is that we do not understand such concepts very well ourselves. So before you try to explain such concepts as "kegare", do a little reading on the subject yourself. Then compare that to Western religious literature. You will broaden your understanding of your own culture.