As far as I know A Link to the Past's Link and Link's Awakening Link is the same Link. After Link leaves Hyrule he goes off on a journey out to sea and gets swept onto Koholint Island after a storm.
LA Spoilers
This can be proven to be the same Link because during the Nightmare battle, Link faces battles from his past experiences such as the battle against Agahnim and Ganon as well as the battles he fough on the Island.
LA Spoilers End Here
As of the Oracle games, it could be the same Link but I doubt it. The official art shows Link as being younger than the Link in A Link to the Past....So I would place the Oracle games after ALttP and LA...Link could already be a hero in the oracle games as he's called by the Triforce, but than again the triforce symbol on his hand could have awakened him as a hero so i believe the oracle Link is a new incarnation!
You're right, he looks a little younger, but it may be just an artistic choice of the developers, it may not be relevant to the story. Anyway, the ending of him leaving on the ship was said to be a voluntary reference to LA, so I think they just retconned everything. Link also fought Agahnim and Ganon in the Oracles, have you forgotten? Ok, that one in Seasons was just an enemy with the same sprites and same attacks of Agahnim, not truly him, but so was Nightmare's form! Also you're missing one point in LA's plot: as said in the manual, Link was RETURNIG from a journey when he end up in Koholint, so the story would be incomplete without OoX. LA's manual also says that Link became the legendary hero and defeated Ganon, but so he did in OoX.
Anyway your points about the awakening of the hero in Link trough the symbol are absolutely fair.