The unevenness is caused because the pendulum does not lift the escapement evenly in each direction so that as it swings in one direction it only just lifts the escapement towards the end of its swing, dropping it prematurely as it begins to swing in the opposite direction. Your solution of wedging the clock on one side had the effect of moving the escapement to a position more central to the pendulums swing. Some pendulums have an adjusting screw to the side of the linkage between themselves and the escapement which can be used to produce an even beat. Have a look to see if there is one on yours. However unless very extreme this would be unlikely to cause the clock to stop and you should still be able to get it to run by wedging so I suspect that, in addition to it's other problem, it requires cleaning - you do say it is old and an occasional service is certainly called for. Usually best to get a local clock or watchmaker to deal with this because simply oiling an already dirty mechanism can do more harm than good - the oil and dirt act like an abrasive and eat away at the clock as it runs. In any case ordinary oil is no good and proper clock makers oil is required.
Some pendulums have an adjusting screw high up near the suspension which can be turned to even up the tick. The unevenness is
Steve Coppard, January 2005