It's better to use one at a time.
First, manage all products in one tool can be much easier and will avoid some duplicate actions.
Second, different tools may cause conflicts that will affect your normal business.
And Oberlo is a Shopify Dropshipping App and AliDropship is a WordPress plugin. They are for 2 different platforms.
For Shopify dropshipping, I will highly recommend ShopMaster for you.
ShopMaster provides a forever free plan and it's easy to use, good for you to start, learn, and scale your dropshipping business. It's free to install the ShopMaster app, saving your budget so you can spend more money marketing in order to get more sales.
ShopMaster is a complete solution for dropshipping, which recommends hot dropshipping products, simplifies your product import and order-purchase, and order fulfillment workflow.
ShopMaster supports you to import from AliExpress, Banggood, CJDropshipping, and 20 more suppliers, bulk edit, and bulk publish up to 300 products to your Shopify store at a time. When you get an order, ShopMaster helps you auto-purchase this order from the supplier within a few clicks.
With ShopMaster, you can also enjoy the supplier product's price and inventory monitor feature, shipment tracking feature, sales report feature, auto-send tracking info to your store, to PayPal, and to your customer's feature.
When you have a question, you can get timely and helpful feedback from our support team. So you are not alone on this dropshipping road.