Roger,
Wow! Very sorry to have missed your earlier post. Let me try to get you straightened out quickly!
Here's 2 quick stabs at how to do both (quickly tested, but do your own testing as well):
Toolbar - Tested and works for us
/components/com_community/templates/default/toolbar.index.php
Around line 77 (in JS 2.2) or 70 (in JS 2.4), you'll see something similar to the below:
<form action="<?php echo JRoute::_('index.php');?>" method="post" name="communitylogout" id="communitylogout">
<a href="javascript:void(0);" title="<?php echo JText::_('COM_COMMUNITY_LOGOUT'); ?>" onclick="document.communitylogout.submit();" class="jsIr"><?php echo JText::_('COM_COMMUNITY_LOGOUT');?></a>
<input type="hidden" name="option" value="<?php echo COM_USER_NAME ; ?>" />
<input type="hidden" name="task" value="<?php echo COM_USER_TAKS_LOGOUT ; ?>" />
<input type="hidden" name="return" value="<?php echo $logoutLink; ?>" />
<?php echo JHtml::_('form.token'); ?>
</form>You'll want to remove everything there (the whole form) except for the a href tag, which you'll need to make a minor modification to the javascript call. When done, all the lines above should be reduced to (mainly updating the onclick call in the remaining line):
<a href="javascript:void(0);" title="<?php echo JText::_('COM_COMMUNITY_LOGOUT'); ?>" onclick="jfbc.login.logout_button_click()" class="jsIr"><?php echo JText::_('COM_COMMUNITY_LOGOUT');?></a>
Hellome - Untested, but hopefully works

/modules/mod_hellome/tmpl/default.php
Around line 177 (JS 2.4), you'll see:
<a style="line-height: 18px;" href="javascript:void(0);" onclick="helloMe.logout();"><?php echo JText::_('MOD_HELLOME_MY_LOGOUT'); ?></a>Update that to:
<a style="line-height: 18px;" href="javascript:void(0);" onclick="jfbc.login.logout_button_click();"><?php echo JText::_('MOD_HELLOME_MY_LOGOUT'); ?></a>There's also a form directly below the line above that should be able to be safely removed. Shouldn't hurt to leave it there either though.
Really hope that helps, but if not, to expedite things a bit, can you post (or Private Message) me the URL of a page you're trying to modify with specific information of what logout button your looking for? The HelloMe and Toolbar both have a logout button, and I should be able to help you modify both, but seeing a specific page will definitely help narrow things down and go quicker in general.
Thank you for patience, and again, sorry for the delay,
Alex