My girlfriend's ex-husband bought four Italian Greyhounds and a Chihuahua during their relationship. The first two had been potty trained, the third may have been, and the last two were not potty trained.
We own a house and they will go to the bathroom and mark inside the house and I'm trying to prevent this, even after having just let them outside. We cage them when we're not home. They prefer to go outside and my temporary fix has been leaving our back door open whenever we are home during the day but they'll still occasionally mark inside.
I don't have any dog training experience and I'm looking for the most effective solution.

How old are these dogs?

Old dogs can learn new tricks. It's a myth that they can't.

Having said that, it will take more time, patience, and consistency, with an older dog than it will a younger one.

Since peeing inside is what they've known all their lives, you'll have to teach them that although that's what they're used to, that's not okay in your house.

You mentioned that you cage them when you're not home. I'm assuming they're in dog crates? Do they pee in the crates?

Are these males, females a mix of both? Are they fixed? How old are they?

Start from scratch. When they go out, you go with them. When they pee or poo outside you praise them like they just cured cancer. Hugs, kisses, high fives, good dog, good dog, such a very very good dog, a treat, and more praise. When they pee inside (since you have more than one dog you have to catch them in the act) a firm NO, then take them outside, tell them to potty, wait for them to potty, and then the praise.

Dogs live to please. They don't misbehave on purpose. But, they are dogs. We bring them into our homes, and expect them to know what's okay and what isn't. In the dog world the rules are very different. It would be like you going to a foreign country. At home you leave your shoes on in the house, in this country it's an insult to leave your shoes on, you take them off outside, by the door. You can't understand the language, so it may take some time before you learn that leaving your shoes on isn't okay. That's what it's like for a dog.

Reward, praise, a firm no but no hitting, no rubbing their nose in it, just a NO, and a correction to show them what you want them to do, and a lot of patience, and they'll get it. Oh, and treats. Lots of treats when they do what you want.

Pictures please?