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Don't know why you want to get rid the Edit link, because it's only show when you login (for your editing convenience =). But if you want to remove it, open "Entry-Info.php" in the include folder and deleted the first line, which is:

<?php edit_post_link(_t('<div style="float:left;"> [[ EDIT ]] </div>'),'',''); ?>

For the Login link, open "Footer.php" in the include folder and delete these lines:

&bull; <?php if($user_ID<>'') {?><a rel="nofollow" href="<?php $redirecto='http://'.$_SERVER['SERVER_NAME'].$_SERVER['REQUEST_URI']; echo wp_logout_url($redirecto);?>">Logout</a><?php } else {?><a rel="nofollow" href="<?=get_option('siteurl'); ?>/wp-login.php">Login</a><?php } ?>