I'll change the order of your questions:
"I read that if earth enters the galactic plane, there will be enough gravitational forces to cause a global cataclysm possibly causing humans to become extinct. Is this true? "
No. It was invented for the Big 2012 Hoax.
The process of going through the Galactic plane is something the solar system does every 30 million years or so and the crossing takes a few millions of years. We are presently 50 light-years "above" the plane and still moving away. If you really want to see what the crossing looks like, you'll have to wait roughly 18 to 20 million years.
"How much gravitational force does the galactic plane have compared to above and below it?"
It is the same as the centre of Earth: When we calculate gravity, we do our calculations as if the Earth's gravity was concentrated at the centre. Yet, if we were able to actually go at the centre, we'd find there is no gravity at all there (all the Earth's mass would be all around us, all the forces canceling each other).
The gravity in the Galaxy is not distributed equally, with a little more of it caused by the mass in the plane. There is enough to cause our orbit around the Galaxy (200 million years) to bob up and down as we go around. We cross the plane about 7 times per Galactic orbit. At the exact moment that we cross the plane, the vertical portion of the acceleration is zero (all the vertical vectors of gravity -- the ones due to the plane -- cancel out).
"Are we due to enter the galactic plane on December 21, 2012?"
No, another 18 million years to go.
'Crossing the plane' is a lie that was invented for the Big 2012 Hoax. It is based on an alignment event which has absolutely nothing to do with the Galactic plane (and which does not happen in 2012). It was 'linked' to the date in 2012 when another book seller said (by mistake) that the Mayan calendar ended on that date.
"And when are humans most likely going extinct"
My guess is around half a million years at most. By that time, all the water will have evaporated from Earth due to the increase in the Sun's output (the rate of fusion at the centre of the Sun will have to increase to make up for the increase of helium at the core). Either we will have adapted to live without water (in which case we will no longer be 'humans') or we will have moved away from Earth (in which case we will evolve to fit our new planet).