Entries from all categories in a category group via URL?
Create a URL structure like this:

yourwebsite.com/categories/groupName

Then in your template:

{% set group = craft.request.getSegment(2) %}

{% set categories = craft.categories.group(segment) %}

Once you have the categories you can loop over them and fetch entries related to each. It may however, be more beneficial to do this via a plug-in where you can construct a more complex query based on the categories and therefore be more efficient.

{% for category in categories %}

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

    {% for entry in entries %}
        // template stuff
    {% endfor %}

{% endfor %}