At what age did Oscar die? And how did he die?

The answer to your first question is not specifically stated in the novel, but it can be deduced by observing the chapter titles as well as their content.  The first chapter is entitled "GhettoNerd at the End of the World 1974-1987" and reveals Wao's "Golden Age" which was when he was seven years old.  Wao was, therefore, born in 1967.  Furthermore, the sixth chapter is entitled "Land of the Lost 1992-1995" and ends right before Wao travels back to Santo Domingo for the last time.  We can deduce that Wao, then, died in 1995 which makes him 28 when he died.  Considering our knowledge of Wao's young life (high school days, college days, teaching days, etc.), that age seems appropriate.

The answer to your second question is also not explicitly stated in the novel.  Oscar dies after being beaten (and/or shot) by Grod and Grundy (minions of "Capitan") in a cane field in Santo Domingo.  The book does not reveal the actual method of death.  However, we know Oscar was pistol whipped the first time he entered the cane field earlier and suffered so severely that it took him a long time to heal.  This time, Grod and Grundy allow Oscar his "last words," and then take his life fairly quickly.  We don't know if he is knocked out first and then beaten, or if he is simply shot.  Either way, Oscar dies bravely in that he returns to Santo Domingo in order to be with Ybon and fully understands the risks involved.