Front wheel drive cars exhibit vibrations from the front of the car by in large due to worn out CV joints. The half shaft has 2 of them and loading (like climbing hills) and turning (which is what a cv joint allows you to do) will give direction dependent vibrations pretty much as a rule.
Changing them is shade tree mechanics level and requires an alignment when done. Of course having tools, a jack and a place to work helps to. Cheap to buy cars are not nescissarily Cheap to Run cars.
Rebuilt half shafts are generally available at auto-parts stores at a reasonable price.

 

Oriellys sold me a driver's side axle for $59 (requires $75 core charge) You can test for a bad axle by driving the car in reverse with the steerring wheel turned. It will make a grinding noise.