To remove the New Page, Recent Changes, and Manage Wiki from the Navigation Space, replace the <$wikiactions$> with the following:
<!-- <$WikiActions$> -->
<ul style="font-size: 120%;"class="WikiActions WikiElement">
<WikiIsEditor>
<li><ahref="<$WikiSpaceUrl$>/space/page"><imgwidth="16" height="16" alt=""src="/i/icon_16_page_add.gif"/></a>
<ahref="<$WikiSpaceUrl$>/space/page">NewPage</a></li>
<li><ahref="<$WikiSpaceUrl$>/space/changes"><imgwidth="16" height="16" alt=""src="/i/icon_16_date.gif"/></a>
<ahref="<$WikiSpaceUrl$>/space/changes">RecentChanges</a></li>
<WikiIsSpaceMember><li><ahref="<$WikiSpaceUrl$>/space/about"><imgwidth="16" height="16" alt=""src="/i/icon_16_gear.gif"/></a>
<a href="<$WikiSpaceUrl$>/space/about">ManageWiki</a></li></WikiIsSpaceMember>
<WikiIsSuperUser><li><ahref="<$WikiSpaceUrl$>/admin/dashboard"><imgwidth="16" height="16" alt=""src="/i/icon_16_bricks.gif"/></a>
<ahref="<$WikiSpaceUrl$>/admin/dashboard">Site Administration</a></li></WikiIsSuperUser>
</WikiIsEditor>
</ul>

To Remove the Tabs, add the following under the Header section in the Theme:
.WikiPageMenuEntries #history { display: none; }
.WikiPageMenuEntries #notify { display: none; }
.WikiPageMenuEntries #discussion { display: none; }
.WikiPageMenuEntries #page { display: none; }


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