Almost all memory is used up by files symply classified as "Other". How do I fix it? Currently using an HTC Desire 510 with Android 4.4.3
It has a total of roughly 3.8 GB interal storage (not counting application storage). But about 3GB are occupied by what the phone considers "Other files", not letting me see which files those are. 

When I connected to a PC through USB I did find a file named ".thumbdata" in DCIM/.thumbnails weighting over 2GB, which I immediately deleted. The empty space in my phone remained unchanged, so I restarted it a couple of times. The file reappeared, now weighting just 30MB, but the source of those used up 2GB is nowhere to be found. What can I do?
.thumbdata is nothing but the thumbnails of the images in your gallery. They are cached into the .thumbdata file.

Other than that, most of the space will be occupied by Apps installed in your phone.

Try clearing the cache of every app that you use and uninstall the apps that you don't need.

Try using ES File Explorer to analyse the files in your phone and get a detailed view of large files, duplicate files, junk files, etc.