You can either set a Group or Record as the Parent of a FeedItem, hence why you don't get an option to share it to a Group on an OpportunityFeed. If you're okay to share the post with a link to the related Opportunity, I can think of a couple of ways to do this.
In its simplest form, you can add a custom field to the objects you want to enable this on, a ShareTo field, the user fills in the Id of the User/Group whose Chatter Feed they would like to share this record to. In an AfterTrigger on the FeedItem, you can then share the post to the user/group Id filled out in your custom field. (Referencing the Opportunity / Lead as a link) This would duplicate the post on both the Opportunity as well as Group.
The other option would be to write a custom VF Section which mimics the behaviour of the standard chatter post publisher where it lets you pick Followers or Groups to share the post with. (Again as a link to the related entity)
Also with the new Chatter Publisher action what you can do is write a Custom Action implemented via a VF Page which lets you pick the Lead / Opportunity record that you want to reference and post it as a link attached to your post. Here you can restrict to just one post that will appear only in the User / Group feed with a link to the entity.
Here's a previous answer to a similar question which might get you started Sharing Feed Item with Chatter Group