In FFVII, it's told that Cloud was a normal person who tried to make it to SOLDIER but he wasn't strong enough. However, after Sephiroth burned Nibelheim, Cloud attacked him, and even though he was just a normal person, he managed to defeat and "kill" Sephiroth. Hojo found Cloud and Zack, both wounded, and took them to Shinra basement to experiment with them. Cloud got infected by Jenova cells, which make everyone in SOLDIER so powerful.

Those Jenova cells got Cloud under Jenova/Sephiroth's mind control several times when the Reunion was starting, and after a lot of events, Cloud and Tifa ended up in the Lifestream. There Cloud discovered his own identity. He and others eventually fought and defeated Jenova*Synthesis and Sephiroth for good, and during FFVII's ending FMV, you see the green Lifestream and red Jenova energy moving around Cloud, and soon only the green energy exists. I'm not sure whether this indicates that Cloud got rid of Jenova cells there or not, but we'll move on to AC.

In AC, Cloud has Geostigma. This is what Kadaj says:
KADAJ: "In the Lifestream... All because Mother's cells are working hard... And yet we... We don't even know where Mother is..."
KADAJ: "I've received a special power from Mother. A power to fight against this planet... which hurts the people living on it. Actually, you all have this power."

Vincent has a different view on the matter:
VINCENT: "The Geostigma... It seems that the cause is an overloading of the system to remove parasites in the body. There's a flow through the body like the Lifestream... It fights against the invasion of harmful substances."
CLOUD: "Harmful substances..."
VINCENT: "The Sephiroth element... Jenova's cells... Call it what you want."

So no matter which explanation is true, Geostigma still has something to do with Jenova cells. Now here's a few questions. Why does Cloud has Geostigma? Is it because of those Jenova cells Hojo put on him in Nibelheim five years before FFVII's events, or was he cleaned of Jenova at the end of FFVII and got Geostigma some other way? How about the children of Midgar, how did they get Geostigma and Jenova cells? I don't buy Kadaj's story about Jenova infiltrating the Lifestream and that way children who are born have Geostigma, since it seems the Planet's power destroys Jenova elements very effectively (notice what the rain sent by Aeris does to Geostigma and the three SHM).

The children weren't Sephiroth clones either, so I don't think they were infected by Hojo or other Shinra scientists. I can only come with the explanation that since Jenova is a virus (it was said in FFVII), the children somehow caught the virus, sorta like you can catch a flu even if nobody puts your body full of virulent cells. And what's up with Sephiroth clones in black capes turning fully into Jenova's control before and during the Reunion in FFVII, but the children are quite resistant to Jenova's control? For example, Denzel snapped out of it when he and Tifa were hurt in Bahamut's blast.

When Cloud was finally healed of Geostigma, he went to fight Kadaj. Now, being healed of Geostigma and the Jenova presence means he no longer has Jenova cells, so doesn't that mean he's just a regular person, so he doesn't have the same strength of a SOLDIER within him anymore? However, Cloud didn't seem any weaker after that. Instead, he seemed a lot stronger. He defeated Kadaj without too much trouble, and he seemed even stronger when fighting Sephiroth. Where does Cloud get that strength if he doesn't have Jenova's cells anymore? By leveling up and training, by keeping his friends inside his heart, what? If it's those things, then shouldn't the other party members also be capable of nearly similar things or even better?

So can someone explain a bit about what makes Cloud so powerful and what Geostigma really is about? And please, try to keep the theories and answers reasonable and within FFVII's world, so no BS things like Gaia theory, crystallized spirit energy, Jewish trees, spheres, pyreflies et cetera.