I have the following xml snippet

<object type="figure" position="fixed" id="fu1">
<objectsource>
<file name="ejb1821.fu1.gif" type="gif"/></objectsource>
</object>

<xsl:template match="object">
 <xsl:variable name="filename" select="translate(descendant::file[@name],

however $filename and $type always end up being empty.

You are selecting the file element, which does not have content.
Try
 <xsl:variable name="filename"
   select="translate(descendant::file/@name,...
instead, same for type.