In our school, the President is the main communicant with the teachers and Principal. She also runs the meetings and keeps all of the committees on their toes and organizes the homeroom parents, who are in charge of hosting parties.
The Vice Pres. needs to know everything that is going on too, so that in the event that the Pres can not be at a meeting, she can step in and run everything. She should also make sure to help remind the Pres. of things that are coming up.
The Secretary should keep minutes of any and all meetings. Make sure they are accurate, because you just may need them some day! You may also depend on her to make copies and distribute them to the students if you do a newsletter or when you are sending out reminders, etc.
The treasurer handles all of the monies and bills and must keep precise and accurate records. She should be in charge of anything financial, such as getting signature cards in to the bank, filing for tax ID (if necessary), etc.
As for elections, I would let the other parents know that they are welcome to run. If you don't get any takers, then decide between the 4 of you who would like to do which job by looking into each others strengths. (I, for example would not like to be treasurer, as I tend to be a little dyslexic with numbers!!! LOL). If you have joined forces last year, you should be able to decide that without much trouble.
Best of luck to you!!!