Sabin has superhuman strength, reflexes of steel, and is the only character that can perform magic without consuming MP. He's saved a life more than once. Is he a super hero? I would say that Sabin is a hero, but I don't think that the creators of Final Fantasy VI created Sabin to be a super hero. I think that all of Sabin's skills and actions can be explained. The Thing can rest easy knowing that he won't have to compete with Sabin for his spot in the Fantastic Four anytime soon.
Saving Lives - There are two instances where Sabin saved someone's life. First is when Celes goes to find him in the World of Ruin, and he's holding up a collapsing house to save a little boy trapped inside. The second is when he jumped out and caught a falling bolder that almost killed his brother in the game's ending. I think that his instinct took over both times, but I think his motivations may have been different. Concerning the kid, I think that Sabin is just a genuinely a nice guy. He was at the right place at the right time, saw he was needed, and wasn't going to stand by to watch someone die if he could do anything to prevent it. The second instance is true in much the same way, but it was definitely a lot more personal to Sabin, as it was his brother who was in danger. In their ending you'll notice that Sabin is able to not only hold the bolder up, but toss it. I think his extra strength came from sensing his brother in danger. That kind of thing happens. Mothers in real life have been able to lift cars off of their kids. That brings me to...
Superhuman Strength - Like I sort of mentioned above, I think that adrenaline is what gives Sabin his strength. He senses danger, and his body is able to do things it normally wouldn't be able to do. In the battle with the Phantom Train, you can make Sabin suplex the train, lifting it up into the air and slamming it down to the ground. There, I would say fear gave him his adrenaline rush. The reason I say his strength is a result of adrenaline is because it is most certainly temporary. When he's holding up the house, he tells Celes that he won't be able to hold it up much longer. She ends up only having six minutes to get the little boy out (and rob the place blind).
Magic - I think magic is just a skill that Sabin is able to acquire, like all of the other characters are able to do with espers. The fact that Sabin doesn't consume MP when he performs magical blitzes is because I think the blitzes are supposed to be thought of as physical attacks. Duncan taught Sabin his blitzes; Sabin was not born with them. That means that any character could have been taught blitzes in different circumstances and would have been able to do the same things as Sabin. They're not a super power; they're a skill.
And so no, Sabin is not the world's strongest man, but he might have the biggest heart.