I believe that your #2 is the best general or default way to punctuate
dates within a sentence, Dick. The date serves as an appositive, renaming
the noun "Monday":
#2
Note that Monday, July 3, is a class day.
I find #3 rather unusual. Because
"Monday" is a proper noun, you would think that the appositive would be
non-restrictive, right? But I can see it as restrictive. And I can
see this usage in particular publications that make concerted efforts to reduce
the space that punctuation takes up.
#3
Note that Monday July 3 is a class day.
BUT your #1 is just non-standard for
me. It compares to *"My friend, Julia went home early." OR *"Christmas,
December 25 is a holiday." It doesn't wash for me unless I see it as an
appositive needing a pair of commas.
#1
Note
that Monday, July 3 is a class day.
[Pertinent principle: When a
date is made up of two or more parts, use a comma to separate the parts when the
parts are both words or are both numbers. Here “Monday” and “July” are adjacent
words in a date.] The comma creates an odd sort of splicing
Take care.
Linda