Category field in entry
It wasn't really clear to me if you want to list only those categories that are related to the current entry
or if you want a list of all categories that are assigned to your sermons.

I dont't think the group filter helps a lot in either case and I'd get the catgories like this.

{% set sermonCategories = entry.series %}


In case you don't want them to be ordered by your manual sort order, you need to
get them using a craft.categories ElementCriteriaModel.

{% set sermonCategories = craft.categories.relatedTo(entry).order('title') %}


To get all the categories you'd query for all of your "sermons" entries first.

{% set sermons = craft.entries.section('sermons') %}
{% set sermonCategories = craft.categories.relatedTo(sermons).order('title') %}


The you can start with your loop. I did some small changes, so that only categories with entries related to it will be shown.

{% for category in sermonCategories %}

    {% set relatedEntries = craft.entries.relatedTo(category) %}

    {# Only show category if there are related entries #}
    {% if relatedEntries|length %}

        {% set image = category.photos.first() %}
        {% set params = { width: 300, height: 200 } %}

        {# If a photo exists, show it, otherwise show a placeholder #}
        {% if image %}
            &lt;img  src="{{ image.getUrl(params) }}" height="{{ image.getHeight(params) }}" width="{{ image.getWidth(params) }}" alt=""&gt;
        {% else %}
            &lt;img  src="/img/cover-default.jpg" width="300" height="200" alt=""&gt;
        {% endif %}

        &lt;ul class="sermonadditional"&gt;
            {% for entry in relatedEntries %}
                &lt;li&gt;&lt;a href="{{ entry.url }}"&gt;{{ entry.title }}&lt;/a&gt;&lt;/li&gt;
            {% endfor %}
        &lt;/ul&gt;

    {% endif %}

{% endfor %}