Learn Spanish (Spain): Los niños volvieron sucios del parque. - The children came back dirty from the park.

In Spanish, adjectives often describe the physical state of the subject while they perform an action. This is called a predicative adjective. Because it describes the state of Los niños as they arrived, it must agree in gender and number, taking the masculine plural form sucios.

Could I use regresaron or devolvieron instead of volvieron here?

You can perfectly use regresaron, which means exactly the same thing as volvieron (to return or come back to a place). However, you cannot use devolvieron, because devolver means to return an item to an owner or a store, not to physically go back somewhere yourself.

Does sucios have to go immediately after the verb?

It doesn't strictly have to, but placing this kind of state-describing adjective right after the verb is the most natural word order in Spanish. Saying Los niños volvieron del parque sucios is also correct, but keeping the adjective right next to the verb more strongly connects their physical state to the action of returning.