What is the all-time NFL modern era (defined as since the 1970
AFL-NFL merger) win-loss-tie records for home teams?

"Home teams" may or may not include games played in a neutral location
in which that team was designated as the host team.

Including playoff records is completely optional; but definitely do
not include preseason records.

I am not a Google researcher, but the answer to your question is the
Miami Dolphins who hold (excluding this 2005 season)a 194-72-1 record
since the 1970 AFL-NFL merger.  The Pittsburgh Steelers are second at
193-74-1.  Try the link below (you may have to type it in but it
provides the information from the Steelers press guide)and then search
for "Heinz Field Advantage" which provides the information above since
1970.

Thanks. www.steelers.com/MediaContent/2005/09/06/06/Steelers_Notes_For_Titans_game_56585.pdf

Check out the websites below, they have compiled lots of versions of
winning records.
http://www.nfl.com/history/randf/records/team/gameswon

http://www.profootballhof.com/history/stats/win-loss_records.jsp

I'm actually looking for the cummulative record of ALL teams, not
which team has the best record.  For example, an acceptable answer
would look like:

Since the 1970 merger, home teams have won XXXX games to date.
Visiting teams have won YYYY games to date.  There have been ZZ ties to date.