Can a Storm make the day longer/shorter? I've read that changes in jet streams can affect the speed that the Earth rotates on its axis, thus making the day longer or shorter?
 A: The Earth's rotation rate and the location of the rotation axis change over time. These collectively are called the Earth orientation parameters. On very short time scales, a day or less, the changes in the Earth orientation parameters result predominantly because of the ocean tides. On the scale of decades to a century or so, the dominant driver is exchange of angular momentum between the mantle and the Earth's core.
At intermediate time scales (a few days to a few years), it's the atmosphere that is the dominant driver of these changes. There are very strong annual and semi-annual variations in the Earth orientation parameters, and these are highly correlated with atmospherical angular momentum. The Madden-Julian Oscillation and El Nino Southern Oscillation also show up in the Earth orientation parameters. On a shorter time scale, a nice big snowstorm across a big swath of the northern hemisphere also can make itself visible in the Earth orientation parameters.
Changes in atmospheric angular momentum on a multi-daily to multi-annual basis correlate extremely well with observed changes in the Earth orientation parameters, and particularly with length of day. Since the location and strength of the jet streams plays a key role in the atmospherical angular momentum, changes in the jet streams do indeed change length of day and the location of the pole.
This is a small effect. The variations in the observed length of day are on the order of a millisecond or two after removing short-term variations due to tides and long-term trends. As the following diagram shows, this correlates extremely well with modeled changes based on atmospheric angular momentum.
http://hpiers.obspm.fr/eop-pc/analysis/excitactive1.php?IB=1&term=1&AAM=1&option=1&dimx=600&dimy=450&langue=1&sel_option1=1&choix=3&trend=1&filter=Select+band+above&P0=1&tr=95&spec=0&freqmin=-10&freqmax=10&choixspec=4&chi_g=1&chi_f=1&TC=433&QC=100&SUBMIT=Submit+request&an1=2009&mois1=1&jour1=1&an2=2013&mois2=12&jour2=31
Image source: http://hpiers.obspm.fr
A: Yes, but only very slightly as the Earth is much heavier than the atmosphere. If you were accelerating at the equator you would exchange angular momentum with Earth, slowing or accelerating it's rotation, depending which way you accelerate. Same goes for air masses, as they accelerate when they warm up or cool down and move more one way as the other way is blocked by mountains, or when they are slowed down by mountains or friction. This probably happen on a daily or seasonal basis.
