Worker thread are not supported on all major browsers yet, so I don't think it will be great idea to involve worker-thread into your design unless you only want to support latest browsers.
All the Ajax calls can be made in parallel, but I guess your problem will be how to know that all ajax call's response has come and data is inserted/updated into browser's database. One way to know that all AJAX responses have been dealt with would be to chain all the AJAX calls. But this will warrant you to hard-code the sequence of AJAX calls into your code-base. If that is not desirable than you would need a separate asynch flow to keep checking if all the AJAX calls have been responded to. You can achieve this by setting a flag for each ajax call and set that to true when the response has been used. Then you will keep checking the status of all the flag in an another flow (started using settimeout).
I am aware of any existing framework to take care of such complex activity, so you will have to write the code yourself for the same. Hope this would have helped you in giving some direction.