If there are a number of links to my web site like this:
www.domain.com/?linkid=101
www.domain.com/?linkid=102
www.domain.com/?linkid=103,
which all get 301ed to the same page, will these be treated by Google and other search engines the same way as links that have no difference in the query string?
Yes they will as a 301 redirect is permanent, so essentially SE's will ignore these pages and only index the page they are redirected to.
There is a slight loss in "link juice" through a 301. So if Site A has the following pages (with all links pointing to it):
www.example1.com/
And Site B has these pages with links going to the following
www.example2.com/
www.example2.com/?linkid=101 (301ed to www.example2.com/)
www.example2.com/?linkid=102 (301ed to www.example2.com/)
www.example2.com/?linkid=103 (301ed to www.example2.com/)
Then Site A will rank slightly better than Site B all other things being equal.
You might also want to consider using the brand new Canonical Link Element on your pages instead of the 301. Here's a video from Matt Cutts of Google explaining why:
http://www.youtube.com/watch?v=Cm9onOGTgeM&feature=channel_page