It is common when freewheels wobble then the gears of the 7-speed cassette would slip and jump from higher to lower and lower to higher cogs of the cassette, it happens due to the random and side-by-side movement of the freewheel, sometimes when you buy old used bikes from mechanics or your friends, then you do not know about the condition of your bike, sometimes the axles of bikes are ruin and damage, as axles are hidden within the hub, you do not know about the condition of these axles, bent and deformed axles would also cause wobbling of the freewheels, in these cases, you have to replace bike axles with a new one to avoid freewheel wobbling.
You have to uninstall all the cogs of the freewheel if it is multi cog freewheel or if it single-cog freewheel then uninstall it from the hub and look closer and deeply, cogs contain nut bolts and the hub contains bearings, inspect all of these small parts to aware about the issue and problem arising within the freewheel, keep the bike on a repairing stand or kickstand and rotate the rear wheel with your hands and check the truing of the wheel also not the truing of the freewheel or cassette, most of the time bearings, cogs or multi cog cassette of the freewheel changes its dimension and moves right or left side from its original recommended position above the hub, which will result in a wobbling of the freewheel hub, so check all of these things, sometimes bearings are old and ruined, change the bearings of the hub and everything will be fine.
Also If the gears are not properly working then when you pedal your bike in a clockwise direction you will notice the right and left side plates of the chain would scratch and rub with the higher and lower cogs of the cassette, there are ratchets which are p[resent in both single-cog and multi-cog freewheel cassette, when time passes after a year or two, these ratchets become totally ruin and are not able to handle freewheel and gear changing phenomenon of the cassette, due to which when you pedal hard on your bike, you will notice your chain would continuously skip and slip within the cogs of the cassette and the freewheel is not able to change the gears between the different cogs of the cassette, all of these things are the signs and indicates that freewheel of your bike is expired and you have to replace your freewheel, also check the chain of your bike, if it is working properly then just buy new freewheel if the chain is also damaged badly then you also have to replace your bike chain with a new one.
Hub Issue:
Most of the time hub is involved in a wobbling of the freewheel, when bike hubs become old these would not participate accurately with the other parts of the drivetrain, and these hubs would start rubbing with the axle and left and right sides of the nut bolts and the other rear wheel parts, in these cases these hubs would require replacement with new expensive brand hubs.
Threading Of The Freewheel:
Freewheels are properly and accurately threaded within the hub axles, and if the dimensions and pathway of the threads of the freewheel are not accurately aligned above the hub axles, it results in a wobbling of the freewheel, it is usually done in the beginning steps when you are inserting and threading freewheel within the drivetrain you have to judge the thre4adings before insertion.
The thread would play an important role in the wobbling of the freewheels because on a normal basis there are two movements of the freewheels, side-by-side lateral movement and up-and-down longitudinal movement of the freewheels, now there are two concepts and two different issues which are responsible for both of these two movements of the freewheel, if the freewheel is not threaded properly on both left and sides, then it will result in side by side movement of the freewheel but if you have placed freewheel at a different angle than the normally recommended angle, it will also result in the up and down movement of the freewheel, these things are checked and inspected when you are inserting freewheel, normally it is a complicated process, it would be better if you can visit your near mechanic shop to solve this problem.
Freewheel Bearings:
Freewheel contains bearings, Their is an exact place and location where these bearings are aligned within the freewheels, most of the time these bearings would slip from their actual places and attain different positions, due to which these bearings would lose their actual position, and also sometimes these bearings come out from the freewheel and fall on trails where you are riding, 50% of wobbling of freewheel would depend on inner bearings.
Derailleur Hanger, Stiff or Stuck CHain Links, And Freewheel Cogs:
Check the position and angle of the derailleur hanger where the chain passes and rotates through small jockey wheels, adjust its position and also check the chain link if bike chain links are seized or stiff then replace these links with new chain links and also check the durability and condition of the cogs of the freewheel cassettes, most of the time cogs are bend and deformed and are not able for the smooth passing of the chain through teeth of the cogs due to which wobbling begins to arise.
Although if your freewheel is wobbling at a smaller angle then it is common because almost every bike’s wheel would cause wobbling of freewheels if wobbling is too much then it might be some problem within the drivetrain of your bike.