Adam Jones - 2 times
The underappreciated Adam Jones is up next for putting up back-to-back 30 homer/100 run seasons in 2012 and 2013. Jones wasn't ever a world-beater in any particular category. He just did everything other than drawing walks very well. He always seemed to be lurking right under 30 homers each season, but only exceeded the number in those two seasons.
Going way back in Orioles history, Ken Williams put up an astonishing season for the St. Louis Browns in 1922. In 153 games, Williams hit 39 home runs, scored 128 runs, and posted a 1.040 OPS. Williams would remain an excellent hitter the rest of his career before calling it quits after the 1929 season, but he never approached his 1922 masterpiece again.
Nearly two decades later, another Orioles player joined the 30 homer/100 run club with Harlond Clift in 1938. Another throwback from the St. Louis Browns days, Clift had a pretty decent career from 1934-1945, but his early days with the Browns were by far the best of his career. Clift also had 100+ walks in six different seasons which is pretty remarkable given the time period.
One of the best offensive seasons in Orioles history happened courtesy of Brady Anderson in 1996. Brady was a decent player overall with a few good seasons sprinkled in his career, but his 50 homers, 117 runs, and 1.034 OPS in 1996 was his best season by a very wide margin. He would play in Baltimore from 1988-2001 before finishing his career with Cleveland.