What can you take/inhale/shoot up with/eat/drink all at the same time to create the best chem cocktail?

I haven't tried this in game yet but Med-X + Jet + Buffout + Slasher + Turbo + Rushing Water sounds like a pretty good combo for a drugged out melee smackdown.

No need for the Jet if you're going with Turbo and Rushing Water.
If you're aiming for an optimal buff to go into a real time melee battle, I'd suggest

Battle Brew(+35%DR)
Med-X(+25%DR)
Slasher(+25% DR + 25% damage)
Turbo
Rushing Water
Nuka Quartz(+6DT)
Whiskey(+5DT)
Wasteland Tequila(+8 DT)

To get the DT increases as posted you need a 100 in Survival though, and for Whiskey & Tequila, you need to have Cass' Whiskey Rose perk.
Be aware though, this basically makes invulnerable, and takes out any kind of challenge.

Med-X, Slasher, Battle Brew for the best defense.
Turbo and Rushing Water for the best offense.

I cleared a good chunk of the Courier's Mile (all the Marked Men, several of the Deathclaws) when I accidently alerted a bunch of them, then ended up taking Rushing Water and Turbo. Felt badass, dropping the entire Mile within ~30 seconds.

Old World Gourmet active.
Wine
Vodka
Atomic cocktail
Sierra Madre martini
Wasteland tequila

Mix all with 25mm of Psycho and cause more trouble than you can forget.

or

Mix all with 25mm of Med-X and forget all the worlds troubles.

Here's what I get hopped up on before I bust heads unarmed

10 doses of Implant GRX
Battle Brew
Black Blood Sausage
Buffout
Daturana
Healing Poultice
Med-X
Nuka Cola Quartz
Psycho (to cover the Slasher wearing off)
Rushing Water
Sierra Madre Martini
Slasher
Thick Red Paste
True Police Stories
Wasteland Tequila
Weapon Binding Ritual
Whiskey
Yao Guai Meat