My junior high mascot wasn’t weird as much as it was lame: The Eaglets (Eagles being our high school mascot). And the colors were blue and orange (???).
And there’s always my school’s mascot, the Hokies, as explained by Cecil here.
The Flames are an NHL Hockey Team. It must be a tough name. Oh wait, what am I saying? I’ve forgotten about the Blue Jackets. “Oo, I’m scared a of a cold weather garment.” Carry on.
I saw a bumber sticker one for a HS football team–they were the Fighting Cocks. (mdf, could the Chanticleers have originally been the Cocks? The team chanticleer means rooster, not chicken)
I have known several schools that were the “Trojans”. Would be a fantastic game.
The Monmouth (IL) Zippers!
Cheerleading has rarely been offered headier (drumroll) possiblities.
Veb
My elementary school was the Black-eyed Saints. Yes, it was a Catholic school, as a matter of fact. 
My college had one of the stupidest mascots I’ve ever dealt with: The White Mules, with the women’s sport teams known as The Lady Mules.
Of course, my high school, being named Notre Dame, had the classic Leprechaun/Irish dude. At least one of my schools has a vaguely normal mascot.
I went to a school for a couple of years where the team name was the Rockets. Granted, the entire school only had about 150 kids in it, but seems like they could have done better.
My college mascot was the Saluki. GO SIU-C!
I used to know a guy from Blooming Prarie, MN. His high school’s mascot was…ready for this?
The Awesome Blossoms
I believe their colors were black and white or something similar. Not very blossomy…
Here in Yuma, Arizona, the teams at the oldest high school in town (Yuma High, of course) are called the Criminals. The mascot is a mean-looking guy in blue-and-white prison stripes.
The name comes from the fact that when the school was founded almost a hundred years ago, they didn’t have a school building yet, so they held classes in one of the buildings at the Territorial Prison.
And here at Arizona Western College, we’re the Matadors.
Dr. Rieux, class of '78 (and '79–but that’s another story…)
This isn’t so much strangest so much as it is just tasteless. I knew a girl from Mullins, South Carolina, and fifty years ago, her school had no money for a sports program, so they got sponsered by a local tobacco company. Their mascot was a cigar store Indian, and their team name was the Aucs, short for Auctioners (sp?), as in the tobacco store auctioners.
Buffalo, New York is the Strange High School Mascot Center of the Universe ™. Take, for instance …
Hutchinson Central Technical Engineers
City Honors Aces (now Centaurs … yawn!)
Grover Cleveland Presidents
South Park Sparks
McKinley Vocational Macks
Riverside Frontiers (shoulda’ been “Heshers”)
The best, or the worst depending on how you see it …
Lafayette Violets
The one high school in the area that tended to be dominant in most sports, though, also had the most unlikely name – Sweet Home.
Ok, brace yourselves, because I’m about to reveal the most awe-inspiring and terror-invoking school nickname ever!
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.Ya ready? It was the name of my high school team.
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Here it comes!
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THE TEDDIES!
Oh, yeah, you’re shaking in fear now!
I went to Theodore Roosevelt High School in south Minneapolis.
Be afraid! Be very afraid!
(We always thought that the cheerleaders should wear clothing appropriate to the team name, but even in the sexy 60’s, the school wouldn’t go for it.)
in Utah they have the following:
The BeetDiggers
The Farmers
My high school in Rhode Island had the ever so brave name of The Clippers. Yep. Our mascot was a boat.
Well, I always found it a bit odd that Burlington H.S. in Vermont (where I spent some time a few years back) was the “Seahorses” when they are not anywhere near the sea. (Unless, of course, there are seahorses in Lake Champlain; I never checked…)
I was a Monroe High School Trojan, which made decorating homecoming floats easy, let me tell you!
Here in Columbia, we have the Hickman High Kewpies. It’s possibly the least threatening mascot ever.
Similar want of geographical logic hasn’t stopped hundreds or thousands of high schools from adopting “Pirates” or “Buccaneers” or similar nautically themed figures as mascots, much less Oglethorpe University (in most decidedly landlocked Atlanta) from calling their sports teams the Stormy Petrels.
As a proud Banana Slug, it is my duty to point out that this is a university mascot, not high school.
Like Juniper, my HS mascot was the Trojans. I was in the marching band, and our fight song was “Fight On”, the fight song of the USC Trojans. My dad, who attended both UCLA and UC Berkeley, often bemoaned that his daughter was forced to play that song.
Vaguely being the operative word… 
Pekin, IL’s high school team name used to be the Chinks! It was changed to the Dragons in the late 70’s-early 80’s iirc.
My mom and dad live in Morton - whose mascot is the Potter - a weird looking guy with a bean pot for a head. Uh-huh. The girls’ teams are the Lady Potters.
–tygre, whose children will be Springfield Senators, as if that’s any less lame…
The Butte Pirates from Butte, MT.
I’m not kidding.
http://www.d111.k12.id.us/BHS/BHS.htm
I think that shows very little foresight.
There’s also the Belfry Bats.