You should be able to do this with the existing classes by using descendants. I used this sort of trick on part of the board index, for instance.
Taking the main calendar as an example you could use this to target standard text:
.days {color: whatever;}
and this to target links in the day blocks:
.days a:link, .days a:visited {color: whatever_else;}
For the admin blocks in question the markup is this bit:
<div class="windowbg2 quick_tasks">
<div class="content">
<ul id="quick_tasks" class="flow_hidden">';
foreach ($context['quick_admin_tasks'] as $task)
echo '
<li>
', !empty($task['icon']) ? '<a href="' . $task['href'] . '"><img src="' . $settings['default_images_url'] . '/admin/' . $task['icon'] . '" alt="" class="home_image" /></a>' : '', '
<h5>', $task['link'], '</h5>
<span class="task">', $task['description'], '</span>
</li>';
echo '
</ul>
</div>
</div>
Which is pretty crappy markup since it's still polluted with SMF 2.0.x crap and really could do with a bit of an axe murder, but anyway....
...you can target stuff in that too.
Example for the header link for each block:
#quick_tasks h5>a:link, #quick_tasks h5>a:visited {color: whatever;}
For just any link elsewhere in the block:
#quick_tasks a:link, #quick_tasks a:visited {color: whatever;}
For text, which would be in the task spans:
#quick_tasks .task {color: whatever;}