[Meela]

I'm no expert, but I'll help as much as I can.

His many names come from his many identities and roles in life, I believe. For example, he acquired the name Thorongil as a cover for his true identity when he served Thengel of Rohan and Ecthelion II of Gondor.
Estel was his 'elvish' identity, for when he lived with the elves, and the fact that it means hope may have been to signify his important role in the future of Middle Earth. Wingfoot was a nickname, and I assume he was given many nicknames by people as they met him.
His importance is that he is the one who can claim the throne of Gondor and re-unite Middle Earth. The time of the War of the Ring is when the need for a king is greatest, so he must be the one heir in his line of fathers to actually come forward and make the claim.
His significance of being of the line of Isildur is that it shows his claim to the throne. I suppose it is always 'of the line of Isildur' because Isildur was the one who claimed the Ring, and bound all his descendants to its fate also.
This relates to why he doesn't claim the Ring. He knows what it did to Isildur, and he knows it is in his blood. He must resist the Ring, or he will share Isildur's fate and become corrupted, and he will not unite Middle Earth.
This is also one of his strengths, and a weakness. His strength is that he resists the Ring, and his weakness is that he is vulnerable to it, because of his bind to it.
I don't know any other significant strengths or weaknesses.
Hope that helped a little.