State channels don't really need or have a "direction" because they are a generalization and more powerful version of payment channels.
For example, the lack of "full" state is what may have led to the unidirectional and bidirectional terms. From this perspective, consider a unidirectional channel as one whose state is simply one value: "Alice's payment to Bob". Or consider a bidirectional channel as one that has 2 values: "Alice's balance" and "Bob's balance".
"Direction" is also different from how many parties can be participate in a state channel. You can have multiple parties in a state channel by setting it (usually a smart contract) to be updatable by multiple parties.
When a node goes offline, it can still receive "transactions" the same way that you can receive a token without needing to be online. If you mean will the node still be able to route transactions on the network, then it would not be able to. When there are disconnections, nodes need to find other peers along the channel path.