You may need to rawurlencode() the string before you send it, this will change the whitespace and other strings like '&' into their HTML safe versions...
So try this instead...
<input type="button" onClick="parent.location='edit.php?Devicename=<?php echo rawurlencode($DeviceName) ?>&EventDesc=<?php echo rawurlencode($EventDesc) ?>'"
value="Edit">
You shouldn't have to use rawurldecode() do decode the strings as php normaly does this conversion from what I know, thou if it comes out funny give it a try anwyays, couldn't hurt it 🙂