You need to move the logic inside the variable, something like below:

<xsl:variable name="newURL">
    <xsl:value-of select="$url"/>
    <xsl:if test="child::area">
        <xsl:text>?area=</xsl:text>
        <xsl:value-of select="area"/>
    </xsl:if>
    <xsl:if test="child::action">
        <xsl:text>?action=</xsl:text>
        <xsl:value-of select="action"/>
    </xsl:if>
    <xsl:if test="child::page">
        <xsl:text>?page=</xsl:text>
        <xsl:value-of select="page"/>
    </xsl:if>
</xsl:variable>
<xsl:value-of select="$newURL"/>