Try some rubbing or denatured alcohol. Pour a bit on the carb barrel and gently try moving it. Don't force it or you might break the throttle arm. If you can get a bit of movement, pour in a bit more alcohol and keep gently moving it back and forth. The alcohol will cut the hardened oil.

If this doesn't work, put the engine in an oven at about 300 degrees for about 10 minutes. The heat will loosen the oil. Once the engine is hot, take it out, the carb will move while it's hot. Immediately apply some alcohol and move the throttle back and forth. Keep adding alcohol and moving it until the alcohol comes out clear. At this point, put it back in the oven for another 5 to 10 minutes to evaporate the alcohol, and then oil it up. I've had to do this to a couple engines, worked like a charm every time.