Is there any truth to the commonly accepted predisposition that 7up
and other clear sodas are, compared to plain water, better or even
helpful when sick with certain illnesses like moderate to severe
colds, influenza, or sore throat? If so, why is this? If not, what is
best to drink while sick with such illnesses?

The following site discusses some benefits of consuming clear liquids
to help combat a common cold:

http://www.the-health-pages.com/education/common_cold.html

and also to combat the flu:

http://www.tarunaoils.com/articles/stomach-flu-symptoms.asp

However, neither site says that sodas like 7-Up specifically contain
an ingredient that combats a flu or cold.  You should consume liquids
(preferably water) to keep hydrated and to help flush out wastes from
your body. 7-Up may also help if you have some nausea along with your
symptoms.  But I'd suggest to gargle with saltwater or dilute hydrogen
peroxide to keep your mouth and throat as clean as possible. Sodas-
which contain sugar- do not keep your mouth clean.  They also contain
carbonic acid, which isn't a good thing for the tummy or your teeth. 
Stick to water and chicken soup.


Incidentally, another urban myth is that sodas like 7-Up can help
prevent pregnancy. That myth is dispelled at:
http://www.bellaonline.com/articles/art11626.asp