I googled and now realise AOMP3 is allofmp3.com, the Russian site of disputed legality in the rest of the world. I don't understand what OE means, but I guess that regardless, it's one-file-per-track MP3, not one-file-per-album plus CUE sheet to provide the track positions.
MP3 isn't gapless, and requires a workaround.
Workaround 1: Get a player that supports gapless info embedded in the LAME tag. Foobar2000 is one, and as eofor points out below, iTunes and Winamp are others. There aren't all that many, but iTunes is highly popular. If the files don't have the appropriate gapless info, you can try to deduce it if you can work out the encoder delay (encspot on a range of files + testing the most likely encoder, plus info from Cuesheet heaven to deduce the original length on CD) then manually enter delay and padding in foobar2000 and get it applied to the file tags.
Workaround 2: Get a player or plugin for a player that works as a gap-killer - something that makes a pretty smart guess where the encoder-related gaps are. Some only remove MP3-type gaps, some remove all silences, even intentional ones. iTunes and some or all iPods have this feature built in, and it's in Winamp (see
Junon's post below). I think it's still available as a plugin for some versions of foobar2000, usually called foo_nogaps.
Workaround 3. If you must play back on a decoder that won't do gapless (like any in-car MP3 hifi I've ever known), you can use a non-transcoding mp3 editor such as mp3DirectCut to join the mp3 files together and then go in and make small cuts of a frame or two at the bit between the end of one file and the start of the next to remove the gaps that are inherent with MP3. With care and luck you'll then end up with a single file of the whole album without noticeable glitches or gaps. If you play this file on a PC as well, you could try to get a CUEsheet. I believe Cuesheet Heaven might help you recover from a lost CUE sheet.