How is the price of gas at the pump directly affected by world events?
 More specifically, how does the price of gas go up overnight when
some significant world event happens?  Why is it not directly
proportionate to the price of a barrel of oil?

I used to work at a gas station and we got a delivery of gas every
week or so.  We were charged for the gas at the time of delivery, so
how can we then say it costs more the next day.  Even if it were that
the price of oil went up proportionately to the price at the pump,
wouldn't it take a little time to trickle down to the pump.  It looks
as though gas companies are very quick to raise the price and slow to
drop it?

I am not really looking for the political answer, just a through
analysis of all the mechanics involved.

http://www.crmbuyer.com/story/34919.html  

This story on the supply chain of the gas industry should give your answer.

The way you pose the question -- that the gas comes in one day and
should be sold the next day at the same price -- is a marxian
critique.  The gas has value independant of the price that you pay for
it.  It is a comodity, representative of the other like components
"refined gasoline with a similar octane rating and detergent
component."  This value fluctuates as both the other quantities of
this like product, and the demand for this product vary.  As recently
demand increased at the same time gas prices increased, would be very
difficult within your implicit framework.  However once we recognize
that expectation of future prices is a determinant of demand, we see
that people were worried that future gas prices would be even higher. 
If this had been the case, the gas would have been a bargin at the
relatively lower $3.50.  This was an increased demand due to
expectation of gas prices at some price higher than $3.50.  The
increased demand at the fixed quanity available of gas(given that gas
comes weekly as you stated) gas stations have to worry about running
out of gas.  If the retail business, which is where the store makes
money, is to be profitable there has to be a positive flow of gas.  To
keep from selling out of gas, the supplier charges a higher price. 
Nowhere in this story did the supplier choose to change a component of
the underlying commodity, they just respond to market forces.  In the
real world application, the gas brokers adjust the price such that
there are not shortages in gas.  In my home town gas at $3.30 was sold
out, indicating that a higher price could have been charged.