If you just want to make the options hidden, then use css to set their visibility or display as hidden.

I've not tried this myself but it should be possible with the function remove_group_tool_option() (see http://reference.elgg.org/group_8php.html#a397a9d3822cb603f4c3910d6fae17b7e). The group options are added by add_group_tool_option() by the corresponding plugins and using remove_group_tool_option() within the init function of your own plugin should disable these options again.

You would have to find out what names the group options are registered as (first parameter used in add_group_tool_option()). For example for the pages group option the name would be 'pages', so removing the group pages should work with

remove_group_tool_option('pages');

The plugins might also extend the 'groups/tool_latest' view using elgg_extend_view(). You can unextend these views again with elgg_unextend_view(), e.g.

elgg_unextend_view('groups/tool_latest', 'pages/group_module');

For activity and the group discussion the tool options are registered in the groups plugin with names 'activity' and 'forum' respectively. For the other group tool options check out the init functions of the corresponding plugins.