If I understand what you are asking, there is no meta-query interface that allows you to query across multiple/all services with one call. Looking at the Resource hierarchy—ArcGIS REST API: Services Directory | ArcGIS for Developers, querying capabilities are only available for services or layers within services. If you want to query all the records behind all the services on a GIS server, you will need to enumerate all of the services and then query against each other.
If it is your server, I assume that you have access to the server (the folder structure which is part of the ArcGIS Server installation). If the data was published to ArcGIS Server with the option to upload the data, it will be part of the service directory and it will be faster to copy the data from there instead of doing multiple REST requests.
