I have just graduated  in Physics and my OPT starts from June. My university offered me a Part-time instructor  and I am going to start this job from June as a Instructor. I am planning to work for one year in my OPT period.This university doesn't sponsor for my H1B visa. But I have read that :

http://internationaloffice.berkeley.edu/students/Current/OPT_new_rules.php

Periods of Umemployment

• Students authorized for 12 months of OPT put their F-1 status in jeopardy if they are unemployed for more than 90 days cumulative.
• Students authorized for 29 months of OPT in total put their F-1 status in jeopardy if they are unemployed for more than 120 days cumulative (see below for more information on the new 29 month rule)

Now , I am wondering whether I can work one year as a Part-time instructor without voilating the New -Opt-rule.  Your valuable comments is highly appreciated.

You should be able to work as a part-time instructor for a year without violating the rule. The new rule doesn't say you should be employed full time; it just says you need to be employed, which you will be.

It should be easier to get H-1B from educational institutions. I am sure there are other foreign nationals working at your uni. Sometimes HR people don't know how to proceed--you gotta lead the way.

Good luck