For the startup Minibrew we developed a simple but effective Shopify connector.
For the moment this connector does not synchronize products between Odoo and Shopify. However your are able to map the products manually. Also when a product does not exists in Shopify, Odoo is able to create the product for you. Reason for this solution was to avoid problems messing up product templates in Shopify when product changes are done in Odoo.
As soon an order is made in Shopify, this order will be pushed into Odoo. For the inventory Odoo is leading and runs a cron job to synchronize you inventory level with Shopify.