I'll say from the start that I'm an only Anime watcher, but I don't mind spoilers at all! I did not like Sao War Of Underworld that much, don't know why, but I feel like Eugeo's character was something that made me like Sao even more than before. Now he's gone, and right when I was about to accept it, Tiese heard Eugeo's voice through the Blue Rose Sword. I heard that in the Light Novel she even saw him? I thought that maybe it was her imagination or something, and went on. But then, a hand gave Eldrie the strenght to live a little more during that "fight", and that arm was Eugeo's arm for sure. I heard that in the light novel his voice could be heard, too. And now I SURE AM CONFUSED. What does this mean? Is a part of Eugeo still alive through the Blue Rose Sword or something? I want to know what is his situation and if he will have any crucial importance again in Sao, I don't care even if you will spoil me all the Light Novel, I just NEED to know what will Eugeo do and if he is still alive. Thanks :)
He's not truly alive. But yeah, a portion of his consciousness remains in the Blue Rose Sword. This can be attributed to
1) His multiple instances of using the Perfect Weapon Control, which is mentioned in the LN (not sure about the anime) as being very dependent on your memories to perform incarnation
2) The way that he even fused with his own sword to fight Quinella.
Again, he's not alive. There's a scene where Higa is on the Ocean Turtle monitoring Kirito's mind and he finds Eugeo's consciousness, but notes that it's coming from the Underworld component (called the Main Visualiser) that's responsible for storing objects, but not the LightCube Cluster, which stores Underworldian souls.
Basically, since memories and objects have the same data format in the Underworld (it's previously mentioned that the Main Visualiser is responsible for Incarnation by utilising people's memories), while Eugeo's soul went on to deletion, his memories remained as an object of sorts.
Remember that divine object weapons in Underworld are created from a memory of what they used to be. When Eugeo merges with his sword the "memory" of Eugeo becomes part of the sword as well.
So he's not alive, he's not coming back. That memory however is going to be import in the finale of war of the underworld, both to bring Kirito back and in the final fight against Gabriel Miller/Subtilizer.