WooCommerce REST API Custom Fields

Answering my own question:

It is possible using the following: (using v3 legacy API)

To send custom fields back to the server: (For Orders)

{
  "order_meta": {
     "key": "value"
  }
}

To retrieve custom fields from server use this filter with your end point:

http://www.example.com/wc-api/v3/orders?filter[meta]=true

This works for Products as well.

As mentioned in the comment after WooCommerce creates an order via the API it will fire woocommerce_api_create_order hook, you can make use of it.

Add the following code to your theme's functions.php file

add_action( 'woocommerce_api_create_order', 'my_woocommerce_api_create_order', 10, 2);

function my_woocommerce_api_create_order( $order_id, $data ) {

     // $data contains the data was posted, add code to extract the required
     // fields and process it as required

}

Similarly look at the code in plugins/woocommerce/includes/api/*.php files, find the suitable action or filter hook for the end point and use it.