One of our dogs once found half a very dead, runny seal, wedged into the rocks at the beach. She tried to pull it free, to bring it home, and when she couldn’t, she rolled in it. A lot.
She stunk to high heaven - dh had taken them to the beach on the train, so had to bring them back the same way, and even our brown lab, who was a connoisseur of gross and stinky, didn’t want to sit next to her.
When he got them home, dh’s plan was to bring her indoors, upstairs, through our bedroom to the en suite, where he could wash her in the shower - but I put the kibosh on that bright idea, and made him hose her off in the garden.
We shampooed her twice outside, and even then she still smelt faintly of dead seal, but was clean enough to go upstairs for a shower - but by then we had run out of dog shampoo, so dh grabbed a bottle of cheap shower gel -Lynx Africa - from the main bathroom, so instead of dead seal, she smelt of teenage boy - which was an improvement, to be fair.
@Cruisem - I second the suggestion of lots of towels, kept near the back door, so you can wipe the mud off as much as possible, if you do need to take TwatDog upstairs for a bath. At least that will help save your carpets a bit.