His first role came in the 1983 hit film Risky Business. However, he is probably best known for his next role, that of Dudley "Booger" Dawson in the 1984 hit comedy movie Revenge of the Nerds and its 1987 sequel Revenge of the Nerds II: Nerds in Paradise. He later reprised his role as Booger in the 1992 television movie Revenge of the Nerds III: The Next Generation and once again in the 1994 television movie Revenge of the Nerds IV: Nerds in Love. Armstrong's typecasting in the role was mocked in The Simpsons episode “E-I-E-I-(Annoyed Grunt)”. His other films include Better Off Dead, Big Bully, One Crazy Summer, Bad Medicine, National Lampoon's Van Wilder, Smokin' Aces, Dodgeball: A True Underdog Story, Jingle All The Way, Southland Tales, and Beer for My Horses. He also had a recurring role as Herbert Viola on the television series Moonlighting, and played the part of Ahmet Ertegün in the biographical film Ray (2004).
He provided the voice for Mr. Moleguaco on the Disney Channel original series The Emperor's New School. Curtis was also in Akeelah and the Bee & Max Keeble's Big Move. He played "Farley", a fictional composite character based on members of Elvis Presley's real entourage in the 1997 cult-comedy film Elvis Meets Nixon. He also had a bit part as "Russel" in the short-lived TV show Reaper.
He voices "Snot" on the animated sitcom American Dad!, parodying his role from Revenge of the Nerds. He also had a role as Double Wide in the cartoon series Stroker and Hoop on Cartoon Network. He appeared in the 2006 production of Akeelah and the Bee as Mr. Welch. He was on VH1's 100 Greatest Teen Stars despite being thirty when he played his first role. He played "Mecklen" in the 2007 film, Smokin' Aces.
In the feature film Ray, for preparation for his role as music executive Ahmet Ertegün, he had the top part of his head shaved to simulate male pattern baldness. He guest starred in episode 10 — "Much Too Much" and had a much smaller part in episode 11 — "Owner of a Lonely Heart" in season two of Grey's Anatomy. Armstrong played a deejay named Jerry Thunder in That '70s Show, episode 315, "Radio Daze."
In 2008, he guest starred in the iCarly episode "iStakeout" as a convenience store clerk who was suspected of pirating movies. In 2009 he appeared in Ratko: The Dictator's Son, and Locker 13. He played fictional astronaut Chaz Dalton on an episode of the TV series My Name is Earl.
2009 found Armstrong playing a paranoid character in a mental institution on the House season six premiere, Broken. Also in 2009 Armstrong appeared in American Pie Presents: The Book of Love, as a teacher obsessed with the principal of the school, and he also appeared as a bumbling bandit in the movie "Gold Retrievers".
In 2010 he made a guest appearance on the television show Glory Daze and currently voices the main character on the animated series Dan Vs. and he also voices Robot in Robot and Monster. He also appeared on Spike TV's Blue Mountain State (S01E11). In 2011 he appeared on an episode of Curb Your Enthusiasm, and has a recurring role as attorney Peter Goldman in season seven of The Closer.
On October 27, 2011, he appeared as himself on the television show Rules of Engagement.
In addition to his acting career, Armstrong's affinity for the music of Harry Nilsson has prompted him to become an expert on Nilsson's work. He has written liner notes for CD reissues of Nilsson albums, and has been instrumental in archival and bonus track preparation for these reissues. Additionally, Armstrong is an avid fan of Washington Irving, Laurel and Hardy, and Sir Arthur Conan Doyle's Sherlock Holmes stories.