If I establish an llc on Jan 1 2014, when is the 800 tax due in the state of California
The 15th day of the fourth month after formation with the SOS, i.e., April 15, 2014, unless it actually began doung business earlier, in which case it is the 15th day of the fourth month after it began doing business. Here is a useful link:
https://www.ftb.ca.gov/professionals/taxnews/2012/November/Article_3.shtml
Note that there is a 15-day short year provision, so you could form your LLC in the last half of December 2013 rather than on 1/1/2014 with the same result, at least for state franchise tax purposes.