I don't understand how a song can be downloaded directly to an iPod, without it going through the iTunes library on your computer and a sync...
But, in any case, you can re-download any iTunes Store purchase using the iTunes Store Purchased screen. So there is no problem with doing the song downloads again. Freeing up space on your computer seems to be problem to solve.
625 songs is actually not that many songs. I have around 6000 songs and my iTunes music library takes up about 40GB of disk space. If they are typical formats, such as MP3 or AAC, YOUR music library should only take up around 4 to 5 GBs. You can look at the bottom of the iTunes screen showing your iTunes Music library to see how much disk space it used.
Therefore, freeing up space on your computer's hard drive will probably involve mostly deleting OTHER files you no longer need (not files related to iTunes). Once there is more free space on your computer's hard drive, you can download more songs from iTunes.
Alternately, you can move your iTunes Media folder to an external hard drive volume (if it's convenient to have an external drive attached). Apple has these articles to explain how.
http://support.apple.com/kb/HT1364 <- For Windows
http://support.apple.com/kb/ht1449 <- For Mac