In the scene where Clemenza is showing Mike the gun in The Godfather he says it's been 10 years since the last war, and in a deleted scene Mike asks Sonny if this is gonna be an all-out war like the last time. What war are they referring to? Is it in the novel?

the 5 familys war

I remember in the novel a war in which the Don was shot and Sonny took command of the family for a short time until the Don recovered. That was when Sonny showed his brilliance in war. Is this the war that they are referring to that happened 10 years ago?

There are many anomalies re. dates. The novel refers to "the great war of 1933," which Vito won by killing his arch-enemy, Maranzano, on New Year's Eve 1933. In the movie (and the novel), Vito is shot shortly before Xmas 1945. Therefore, Clemenza's statement in the film that the last war was "10 years ago" seems inaccurate.
But the novel goes on to say that, after Vito killed Maranzano, he set about "pacifying" the other families and the free-lance "black-handers", a process that took three years. During that time, "a group of mad-dog Irish stickup artists" managed to put a shot in Vito's chest, setting the stage for Sonny to show his "genius for urban guerilla warfare" from 1935 to 1937. The Corleones' hold was consolidated by 1937, says the novel.
To get to the point (and I'm sure you wish I would), Clemenza's 10-year statement may have been in the ballpark after all.

but in 1933, would that have been the famous Olive Oil wars?

"Olive Oil wars?" Not sure where that's mentioned.
Here's another date anomaly: At Connie's wedding, Michael explains to Kay that his father was shot "Fifteen years ago." The wedding was in 1945, so that date would put the "mad-dog Irish stickup artist" shooting to 1930, instead of 1935--the time frame mentioned later in the novel, when Puzo goes into the Don's background.

I believe that this was also the time and the reason that Luca Brasi singlehandedly wiped out the Irish gang.

Don Cardi