<xsl:apply-templates/> This command means "run through my XML and match as you find the nodes." In your case, the rendering will be in the order of appearance in the XML. If the DX_NO node appears before an EMAIL node, then it will show up in the HTML that way.
You need to invoke the templates directly:
<xsl:template match="/">
<xsl:call-template name="showdata"/>
</xsl:template>
<xsl:template name="showdata">
<p>
DX No:<xsl:value-of select="DX_NO"/>
</p>
<p>
e-Mail:<xsl:value-of select="EMAIL"/>
</p>
<p>
Facsimile:<xsl:value-of select="FAX"/>
</p>
<p>
Event:<xsl:value-of select="EVENT"/>
</p>
</xsl:template>