Can you do anything if youre not technically in charge..? ?

I'd tell your sister that you can't guarantee her dog will be cared for it it's left in your dad's house. Explain that he's a blackout drunk and you're often busy and that if she cares about this dog she needs to keep it with her and take care of it herself. 

Let the dog tear up the house. It’s your dads house , not yours. Stop cleaning up after the dog, not your dogs. Just stay in your room.

Your dad is not being put out bc YOU are taking care of things. Stop it! As long as your dad isn’t inconvenienced he won’t have a problem with your sister dropping off the dog

You should tell your dad that you absolutely will not care for your sisters dog without being asked. If the dog pees on the floor, leave it for dad to clean up. Tell your sister the same thing. She shouldn’t have a dog if she isn’t prepared to take care of it. Tell them both that you have no intention of feeding, walking, or cleaning up after any additional dogs unless you specifically agree to it. If your dad keeps agreeing to care for the dog, but not actually doing it, just keep putting the dog in your dad’s room. Maybe your dad will change his mind when he steps in pee or poop in the middle of the night, or the dog won’t stop barking. As long as you keep stepping up to care for the dog, they’ll keep dumping it on you. 

Typically

the ones who are not technically in charge

are the ones who do the most.