Are "three way" trades allowed in Catan?
No (or yes, depending on how you define a single trade).
The person whose turn it is can trade. Each trade is with that person and one other person.
If you can accomplish what you need in a series of trades, you're welcome to try. But any promise of future trade is non-binding: your later trading partner may legally decline the trade when it comes time.
Rules:

Important: Players may only trade with the player whose turn it is.

Also note that each trade has to involve a card from each player in the trade. You can't just give a card away for nothing in return.
So in your example:

A trades ore to B in exchange for brick.
A trades brick to C in exchange for wheat.

This is legal, but it is two separate trades.
There are no escrow rules: C is free to decline the trade after trade 1 has happened.