(...)
And I need to transform this to RDF.

Your expected output is missing... but I can provide some hints based
on your xsl:template:

<xsl:template match="gemq:catalogingOrganization">

1) For the sake of clarity, you should replace this choose inside a
single template by different templates with different XPath matches,
as described previously.

<xsl:choose>                                                    <xsl:when
test="gemq:catalogingOrganization/foaf:name">

2) It is very important to note that the XPath expression in the match
(here "gemq:catalogingOrganization") defines the context for
expressions inside the xsl:template.
So when you write "gemq:catalogingOrganization/foaf:name", you are
testing whether current gemq:catalogingOrganization has (again) some
gemq:catalogingOrganization child with foaf:name grandchild.

You should either write simply "foaf:name" (or the longer
"self::gemq:catalogingOrganization/foaf:name" which is what you
meant).

        <xsl:value-of
select="normalize-space(gemq:catalogingOrganization/foaf:name)"/></xsl:when>
               <xsl:when test="gemq:catalogingOrganization/foaf:phone">
        <xsl:value-of
rdf:resource="{normalize-space(gemq:catalogingOrganization/foaf:phone)}"/></xsl:when>

3) you cannot output an rdf:resource element this way. xsl:value-of
returns the text value of the XPath expression in the "select".

To output an rdf:resource element, simply write
<rdf:resource>
(...)
</rdf:resource>

Optionally, you can add attributes simply using "attribute value
templates" (an expression relative to the source document inside curly
brackets):

<rdf:resource id="{foaf:name}">
(...)
</rdf:resource>

Finally, use xsl:value-of only to output the text of the result element:
<rdf:resource>
 <xsl:value-of
select="normalize-space(gemq:catalogingOrganization/foaf:phone)" />
</rdf:resource>

        <xsl:when test="gemq:catalogingOrganization/foaf:homepage">
        <xsl:value-of rdf:resource="{normalize-space(gemq:catalogingOrganization/foaf:homepage)}"/></xsl:when>
        (...)
</xsl:template>

[1] XSLT Tutorial
http://www.w3schools.com/xsl/

[2] XSL Transformations - from Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/XSLT

[3] XSL Frequently Asked Questions - maintained by Dave Pawson
http://www.dpawson.co.uk/xsl/

[4] Jeni's XSLT Pages - Jeni Tennison
http://www.jenitennison.com/xslt/index.html

books:
[5] Beginning XSLT by Jeni Tennison
http://www.amazon.com/gp/product/1861005946/103-9672661-7999067?n=283155

[6] XSLT 2.0 Programmer's Reference, 3rd Edition by Michael Kay
http://www.wrox.com/WileyCDA/WroxTitle/productCd-0764569090.html

and reference material:
[7] W3C Recommandation - XML Path Language (XPath) Version 1.0
http://www.w3.org/TR/xpath

[8] W3C Recommandation - XSL Transformations (XSLT) Version 1.0
http://www.w3.org/TR/xslt