In case with native items ( added by other plugins within the software), you will need to add a target_blank attribute within the <a> tag. For example for videos added via "Video" plugin you will need to edit ow_plugins/newsfeed/views/formats/video.html and add targer_blank attribute into the <a> tag in bold:

 <div class="ow_newsfeed_item_content">
       <a class="ow_newsfeed_item_title" href="{if !empty($vars.url)}{$vars.url}{else}javascript://{/if}">{$vars.title}</a>
        <div class="ow_remark ow_smallmargin">{$vars.description}</div>
        <div class="ow_newsfeed_action_activity event_newsfeed_activity">[ph:activity]</div>
    </div>

For images, you will need to edit ow_plugins/newsfeed/views/formats/image.html and so on.
Just look into all .html files within the /formats/ folder, you will need to edit all of them.

In case if "Photo" and "Video" plugins are disabled ( deactivated) on your site, then links added into the newsfeed will be added by core feature called "oembed": ow_system_plugins/base/views/components/oemed_attachment.html . As far as I can see from the code, this feature should already open links in new tabs, since the .html code already contains target_blank.