Formal:
* Privy
* Toilet (in a historical context)
* Latrine
* Outbuilding (if it's not specifically for toileting)
Informal:
* Toilet (if it's clear you're not talking about the indoor kind)
* Crapper (slang)
* Head (nautical slang)
* Dunny (Australian slang)
* Backhouse
Other related terms:
* Outdoor toilet
* Composting toilet
* Dry toilet
The best synonym to use depends on the specific situation and the tone you want to convey. For example, "privy" would be more formal than "toilet", and "crapper" is very informal and might be considered offensive in some contexts.