Learn Spanish (Spain): ¡Vaya timo! La habitación está asquerosa.

Both are perfectly fine and mean the same thing, but ¡Vaya! followed by a noun is a very common way in Spain to express a strong reaction like surprise, anger, or admiration. Here, ¡Vaya timo! strongly emphasizes the speaker's frustration.

Would vaya change if the noun was feminine or plural?

No, it stays exactly the same. Even though timo is masculine, vaya is a fixed exclamatory word here. You would say ¡Vaya casa! (What a house!) or ¡Vaya zapatos! (What shoes!) without changing vaya to match the gender or number of the noun.

Where does the word timo come from?

It comes from the verb timar, which means to swindle, scam, or cheat someone. In Spain, calling something a timo is the standard, everyday way to say it is a rip-off.

Why do we use está instead of es for a disgusting room?

We use está (from estar) because the speaker is talking about the current physical condition of the room. It implies the room is just dirty right now. If you used es (from ser), it would mean the room is inherently and permanently a disgusting place by its very nature.