If the USB is properly formatted and if the style files are SFF1 style files, the styles should show up when you select the "Load STY" file function while the USB is inserted. However, there are a few possible reasons why they might not show up.
(1) Contrary to what some people advise, the USB stick should only be inserted or removed while the PSR-E keyboard is turned on. This might be different from higher-end models, so always check the owner's manual for your particular model and follow the guidelines that it specifies. The two important things to note with regard to inserting or removing the USB stick are that (a) when you insert the USB stick you must wait several seconds while the keyboard reads it, during which time the upper left corner of the LCD panel will display a flashing USB indicator, which will stop flashing when the keyboard has finished reading the USB stick; and (b) when you save data to the USB stick, wait until the keyboard has finished writing to the USB stick. Do not remove the USB stick or turn off the keyboard while the keyboard is reading from the USB stick or you could corrupt the keyboard's memory; and do not remove the USB stick or turn off the keyboard while the keyboard is writing to the USB stick or you could corrupt the USB stick.
(2) If the USB stick is not formatted properly-- that is, if its file system is not in a format that the keyboard can understand-- then the keyboard will not be able to access it. If you format the USB stick using the keyboard, the keyboard will format it using the file system that it understands; but if you format the USB stick using a computer, it might get formatted using a file system that the keyboard can't understand.
(3) The PSR-E models cannot use the SFF2 style file format, also known as SFF-GE ("Style File Format - Guitar Edition"). The style files must be SFF1 style files or the keyboard won't be able to use them. It should still be able to see them on the USB stick, but it won't be able to play them. Jorgen Sorensen has a utility that can convert SFF2 style files to SFF1 style files.
(4) The extensions on the filenames must be ".STY"; none of the other numerous style file extensions that Yamaha uses will work. Note that the filename extension doesn't affect the internal style file format, so if you have SFF1 style files that don't use the ".STY" extension then you can simply rename their extensions using a computer.
(5) There must not be any extra periods in the style file's name, otherwise the keyboard will have trouble being able to correctly detect the filename extension. Note that many Yamaha style files include an extra period followed by a 4-character icon ID before the filename extension, such as "4-BeatRock.A123.STY" or something similar. Many Yamaha keyboards use those icon IDs to tell them which icons to use when displaying the style file's name in the LCD panel display, but the PSR-E models don't use special icons like that and the icon ID will confuse the keyboard because it will see the period that's in front of the 4-character ID and think that everything after the period is the filename extension. If you have style files that have these icon IDs in their filenames, use a computer to rename the filenames and either delete the extra period and the icon ID, or at least change that first period to some other character so it doesn't confuse the keyboard.
(6) The style files must be small enough to load into the available "user style slots" in the keyboard's system memory. The exact size varies a little bit from model to model, but a good ballpark number is 50kB, otherwise the style file might be too large to load into the system memory. If you have style files that are too large to load, you can usually reduce their sizes by using a utility from Jorgen Sorensen to rearrange the style sections and remove any unusable variations. The PSR-E models are limited to using the A and B variations, so any sections for the C or D variations can be deleted to remove any extraneous bytes from the style file.