It does look like its oncidium related. But will be hard to ID other than that.
That reminds me of the large Sharry Baby that Katie gave me. Only I intentionally potted mine in an 8-inch basket and is not yet as overgrown as yours.
This one still has a few seasons to go before I worry about repotting
If you need to repot it, you probably need to break open the wood basket. Or if the roots are not attached to the basket you could gently pull the entire plant up and out of the basket.