Unfortunately, you can’t check the status of your application online so you either have to go to the store you applied to and talk to somebody or call the store and tell them you’re checking on your app.
If it has been awhile since you applied, don't wait for a response from Walmart regarding your online application. Either call the store or go in to see them. There are many instances where people never received a call from them after submitting an online application and only getting the job after repeatedly contacted them. Managers can be busy and forget to follow up.
When you apply, the application stays on file for 60-90 days and if an opening come up they will contact you. Also Walmart will sometimes want you to apply for a role because it actually becomes open.
Some other tips:
More details about the application process can be found here: https://careers.walmart.com/application-process-step-by-step