Phule's Company

Phule's Company is a sci-fi series by Robert Asprin about (what appears to be) a Millionaire Playboy in the Space Legion who gets Kicked Upstairs and in charge of the Legion's worst unit, unofficially called The Omega Company. He has to turn them from a Ragtag Bunch of Misfits into a well-oiled machine, and through the books encounters more and more bizarre assignments and new worlds.

Later books in the series were officially "co-written" by Peter J. Heck. For better or worse, it is very likely that Heck did most if not all the work.

Books in the series:

Phule's Company (1990). Phule gets a new Legion name and takes over the Omega Company, stationed on a swamp planet.
Phule's Paradise (1992). The company takes over guarding a space casino.
A Phule and His Money (1999). The company finds themselves in contest with a planetary government that runs on theme parks.
Phule Me Twice (2000). Robot doppelganger
No Phule Like an Old Phule (2004). Phule Sr. shows up
Phule's Errand (2006).

Tropes used in Phule's Company include:

All-Natural Gem Polish: Lampshaded and averted.
At Arm's Length: People do this to Super Gnat when she gets mad. It just makes things worse.
Berserk Button: Nearly everyone has one, Omega Company or not.
Boobs of Steel: Top Sergeant Brandy is a superior brawler who is described as physically impressive in pretty much every possible way.
Briar Patching: The biker gang that Chocolate Harry joined the Legion to escape catches up with him. After hearing how CH had doublecrossed them, Phule orders C.H. to let them destroy his beloved hoverbike as punishment. Over C.H.'s impassioned protests, the gang takes their revenge. After they leave, we find that Phule and C.H. had planned the whole thing, and C.H. had exaggerated his grief to make sure they were satisfied. Regaining his peace of mind was worth the loss of his bike.
Bullethole Door: Averted.
Camp Cook: Escrima. Cooks like a five-star chef, with an ego to match. Also qualifies as Chef of Iron, since he's a top-notch fighter, including teaching his namesake fighting style to other company members, and is capable of hospitalizing would-be food critics.
Cast Calculus: Or how most of the Omega Mob gets broken down into manageable pairs... as well as non-Legion characters, such as the two IRS agents from A Phule And His Money, General Blitzkrieg and his long-suffering assistant Sparrowhawk, etc.
Corrupt Politician: Governor Wingas, in Phule's Company, licks his lips at the possibility of getting a "campaign contribution" from Phule.
Dating Catwoman: In Phule's Paradise Beeker and Laverna strike up a pleasant relationship despite -- in fact, somewhat because of -- being aides de camp to the leaders of the enemy groups.
Dungeon Bypass: Grenades + Combat Conditions Obstacle Course.
Earth-That-Was: Although Earth and its history are often indirectly mentioned, it is always in the past tense. During the very few times the Earth is directly mentioned, it's referred to as Old Earth.
Eloquent in My Native Tongue: Tuskanini. Translator Microbes avert this for the Gambolts and Sinthians, but not so much for Leftenant Qual.
Elvis Impersonators: Converts to the Church of the King have plastic surgery to take on his features. This leads to a certain amount of confusion, which the Legionnaires eventually use to their advantage.
Fiction 500: Captain Jester, aka Willard Phule, is one of the richest men in the galaxy, which is why he was reassigned to the Omega company instead of merely drummed out of the Legion.
- Actually, it's why he was reassigned instead of being sent to the stockade for several years; the Legion cannot force someone to leave.
Gentle Giant: The pacifistic Volton Tuskanini, a seven-foot-tall warthog who wouldn't fire a gun at the start of the series.
Hover Board: Spartacus, the Synthian, rides one of these.
Huge Guy, Tiny Girl: Tuskanini and Super Gnat.
Intelligent Gerbil: Cat, slug, warthog, lizard.
- All of which are considered racial slurs and discouraged by Phule.
The Jeeves: Beeker, Phule's butler.
Kicked Upstairs: Phule, and how the series gets its start.
Literary Agent Hypothesis: Supposedly, the books are Beeker's recounting of events; the story is interspersed with his personal comments, and occasionally he will explain that he's just inferring scenes he wasn't there for from the things he does know.
Loophole Abuse: The Omega Mob finds itself in a competition against the elite Red Eagles to see who can make it through an obstacle course fastest. Phule specifies that the race will be with "full combat gear and conditions," and the Red Eagles quickly complete it despite carrying a full infantry loadout. However, Phule's company finishes even faster since "full combat conditions" means they can blow up or destroy every obstacle in their way, something the Red Eagles hadn't considered.
Mildly Military: The Omega Squad, though it's used for good once Phule takes over.
Military Brat: Lieutenant Armstrong, apparently; he's one of the more militarily formal Legionnaires as a result.
Misfit Mobilization Moment: The first in the series is either the obstacle course or the massing-of-Mob-members-at-the-airstrip moment, both in the first book. First, when the Mob demonstrated that they (and their leader's methods) weren't completely worthless; second when they fully demonstrate their solidarity/loyalty to their new captain.
- They also get off a good one in the second book when Max kidnaps Phule but neglects to do anything to neutralize the Legionnaires. As Beeker comments, this essentially removes every brake they had.
Mission Control: Mother.
Mundane Solution: Grenades + Combat Conditions Obstacle Course.
Private Military Contractors
Ragtag Bunch of Misfits: The Omega Squad.
Reassignment Backfire: Every. Single. Book.
Red Oni, Blue Oni: Do-Wop and Sushi, for one, the former being hot-blooded, short-tempered, easy-going (when not being Hot Blooded), and impulsive, while the latter starts out like The Stoic (becoming The Smart Guy), is technically adept, and good enough to talk his way out of a riot and into the Yakuza. Of course, they initially dislike each other and attempt to get re-assigned to new pairs, but by the end of the book they're breaking and entering for the good of the Mob. To varying degrees, most of the rest of The Squad is like this as well.
Sassy Black Woman: Laverna Nightingale, if more understated than most, and despite having been initially presented as an Ice Queen.
- "Mother," aka Rose, is a Sassy White Woman -- but only over the radio.
Scary Black Man: Chocolate Harry, although only to non-Legionnaires. Well, he is a Badass Biker in addition to being one of the two main big guys.
Screw the Rules, I Have Money: One of the extremely rare occurrences where this is done by the good guys, for good reasons, usually to get around an Obstructive Bureaucrat.
Shallow Parody: The swipes at Isaac Asimov's Foundation novels in Phule's Errand.
Shown Their Work: Book 2 could easily have been called A Phule's Guide to Fleecing a Casino.
Shrinking Violet: Rose/Violet/Mother off-radio; her first Legion name (Violet) directly references this trope.
Sleeves Are for Wimps: Chocolate Harry...convinces...the tailor that Phule hires that his custom-designed uniform does not need to have sleeves.
Take a Third Option: Grenades + Combat Conditions Obstacle Course.
Take That: After Asprin ran into Real Life trouble with the IRS, an absolutely vicious tax-agency subplot appeared in A Phule and His Money.
Terra Deforming: Phule's Errand introduces the planet Ron'n'art which is totally roofed over, up to a mile from the surface. Making it an extreme example of a Planet City. Ron'n'art is noted as having a richly deserved reputation for decadence, corruption, and paralysis of every agency. If it weren't for the robots and automated systems, nothing would get done and everyone would starve.
Translator Microbes: Translator boxes.
Vibroweapon
The Voice: Mother. A mild subversion since the person exists but is cripplingly shy and will talk freely only when she's on the radio.
You No Take Candle: Subverted. Tuskanini learned the language manually instead of relying on Translator Microbes, and Phule realizes that even speaking stilted English is a sign of exceptional intelligence.