I'm Aria, I'm on the Social Care team at Shopify. :)
Oberlo is exclusive to Shopify. If you wanted to use it on a website other than Shopify, you could do that using the Shopify Buy Button. The Buy Button allows you to manage products in the Shopify admin and display them for purchase on a website outside of Shopify. If that's all you need, you could use the Shopify Lite plan which is $9 per month. The Lite plan allows you to use the Buy Button, have a Facebook store and sell in person.
I hope this helps. We're always here for support if you have questions. :)
What platform is the website built with? Some e-commerce platforms like WooCommerce also have plugins that can import products and descriptions from AliExpress, similar to using Oberlo. If you need help with that feel free to message me.