I don't want to use a 3rd party "deletion app" to delete apps as I don't trust a lot of these types of apps.
Nor should you, since they are not reliable and using them could easily result in a corrupted system.
Do you have a great many third party apps, or just a select few for which you can use each one's recommended deletion procedure?
If you have a large number of them, or if you are not sure what's installed, or if their uninstallers simply don't work (a common characteristic of poorly implemented software) then the most expedient solution may be to create a backup of your existing system, erase it, reinstall OS X, and then reinstall your essential software. If you want to do that, write back for detailed instructions. You will need a device on which to store your essential software, usually an inexpensive external USB hard disk, but which can conceivably be as simple as a USB flash memory stick.