My father was the youngest of seventeen children in a blended family. I had first cousins who were elderly when I was a child.
I was adopted, and didn’t find anybody from my birth family until 2004, so I missed out on years of weirdness (probably).
But almost without exception, every woman in the family had her first child without being married, even when it was a scandal to do it that way. (Some of us went on to marry the father of the child, but mostly not.)
I think I need a diagram…
My father, my mother’s brother, and my mother’s sister’s husband [i.e., three brothers-in-law] all have the same given name. Furthermore, when moving to America, they each chose to make those given names into their official last name rather than first name. Thus, this portion of the extended family all shares the same last name, as in the typical Western tradition, but entirely by coincidence.
My mom’s named after her dad: he was a William, she’s a Willa. Her sister’s name is Alpha, but Alpha’s the second girl in the family.
Mom’s birthday is Dec. 31, her sister’s is two years earlier on Jan. 1. My bro was born on Christmas Day.
My sister had her daughter the day after her birthday, so their birthdays are back-to-back.
I have two older brothers. Except that’s not entirely accurate. My oldest brother isn’t related to me in any way at all - he’s just a really old friend of the family (my true brother’s best friend since jr. high) that we’ve unofficially adopted. By his own choice, he’s broken all ties with his birth family, and calls my parents Mom and Dad, and me and my siblings brother and sister. I refer to his wife as my sister-in-law.
My birth mother gave me up to *her *mother to raise, so I ended up with my sister being my biological mother, and my nieces and nephews being my biological brothers and sisters. Not really too weird.
My birth father was a mystery most of my life. I knew that he was married to some other woman when he got my mother pregnant, left that woman, and eventually married my mother. They divorced after she got pregnant with my youngest sister while he was at sea. (Coast Guard) Like a post upthread, he was drunk when he registered her birth, so instead of being Leah, she turned out to be Leha. Years later, they remarried but only lasted a year before divorcing again. He died two years ago, and we found out that he had been married nine times…once to some Amish woman, and once in Vietnam. I know of half a dozen half-siblings, and may have some in countries far off. I’ll never know.
My mother never knew her birth father. She took his last name, and we’re pretty certain that he married grandma, but they divorced when mom was still an infant – maybe even before she was born.
Nobody ever talked about why he left in such a hurry. It was always treated as a big scandal, and those in the know refused to entertain is as a topic of discussion. As of a couple of years ago, there were only two people on the face of the earth who knew the truth. They both passed away recently.
Paging Sampiro.
I’m not sure they stayed within the parameters of the merely ‘odd’ as the OP asked. But I enjoyed their tales and realize my strange family ain’t all that strange.
I’d say Anaamika definitely stayed within the parameters.
I checked this out with the 'rents. Turns out I am just the only son of an only son of an only son. My ggf had several brothers.
I’m also something of an attention whore, as you’ve no doubt figured out by now. 
That’s in the FAQ, dude.
My mom is the oldest of eight, so my youngest uncle is three years younger than me, and my oldest first cousin is 17 years younger than me. I’m 38, and I have ten os so first cousins who are infants - kindergarten age.
My mom and her stepmother were pregnant at the same time twice, and my mom and I had babies six weeks apart. This is a family tradition that I have no intention of carrying on!
My father is the only one of his brothers who ever really left home, assuming that moving into the upstairs apartment doesn’t count.
My paternal grandmother was born in 1869. She lived with us up until her death in 1961.
In the late 1950s, one of my favorite shows was “The Life and Legend of Wyatt Earp”, starring Hugh O’Brian. I remember that we were watching it one night and my grandmother made some remark about him not looking like that.
Turns out that my grandmother, as a young girl of 9 or so, lived in Dodge City for several months because her father had business dealings there. Earp was a deputy marshal in Dodge City at that to,e and apparently had become friends with her father. He was a guest for dinner at their house pretty much on a weekly basis.
Now, I’m 10 or so when she reveals this. She got huge kid brownie points in my eyes: my grandmother actually knew Wyatt Earp. She said he smoked cigars that smelled like burning horse droppings.
I’m in the FAQ? Kewl! 
Ok I’ll throw out a cute one.
My grandpa, dad, brother and paternal aunt & uncles all have really boring, all-American names. Bob, Steve, Mike, Ann, etc.
However, they all married people with non-standard names: Lovina, Mary Kahl, Yvonne, Paulette, Vlado and Adena.
On my mom’s side, my mom’s two sisters married old hillbillies that went by nicknames - Smitty and Whitey.
All of those spouses are American born and raised in boring old American families except for one. They just have weird names for boring American people.
Also, my paternal grandma was sick a lot when my dad was a kid. They belonged to the Mennonite church, and when grandma had to “go away” for stretches, the church sent over a young lady to take care of the kids and the house. Shortly after grandma died in 1986 (my 7th birthday), grandpa looked up this Mennonite lady, found she had never been married, and married her within a year. They’ve been together ever since living in the farmhouse her father built for her family back when they were still Amish (her family converted when she was 18).