Eric, if it's a source-tracked project, the CLI's source tracking should take care of it. For a non-source-tracked project like you're describing here, the easiest way is to use IC's Retrieve Metadata action configured as follows:
Notice that it's configured so only server-only metadata will be included. This will work well for wildcard metadata types and if orphaned metadata is included in your subscription, but if not, you may also need to uncheck Subscribed Only and perhaps change Contents to Custom. Finally click Retrieve for Merge so that you get the diff tool for reconciling differences.
Once the retrieve has completed, you can use the IDE's directory diff tool as follows:
Notice that it's filtered to show only files that exist exclusively in the project and weren't included in the renewal (the blue right arrow and equals are disabled, and the green left arrow is enabled). That will show you "orphaned" project files which you can then select. Once selected, right-click and choose Set Delete, then finally click Synchronize Selected (the old-school play button) and all of the selected local files will be deleted.
To perform a full project/org synchronization via the project's configured metadata subscription, basically do a full Retrieve for Merge, carefully merge files that are present in both the org and the project, add org-only files that were retrieved, remove files that are present only locally, and afterward use Deploy Modified Metadata to update the org with the project's reconciled state.
Hope that helps! Let me know if you have other questions.
Regards,
Scott Wells