the oscillation you see in pic 1 is the sinewave from your AC bulb

1/0.020 = 50Hz
the oscillation on the pic 2 is a capacitive coupling of the sensitive input and high gain amplier with your finger. Your body create a big antenna
as explained in other topic 1M is a very high gain!
To give you an idea my laser harp sensor "see" scattered laser light at 3 meters with only 220K of feedback in my I/V converter!
the LM324 in not rail to rail input/output and even if they said "low voltage" it's for biased input not from groud to V+
it's for AC signal with V+/2 bias at the input and the output will move around the Vsupply/2. this is why we must use AC coupling capacitors in that case.
for your application you must use a rail to rail in/out amplifier or +8v/-2v supply voltage to get à +5V swing voltage at the output.
look this circuit:

R3 and R4 makes a voltage divider to VCC/2 for the V+ input. it's a single voltage application. and you have AC coupling capacitors (C1 and C2) at the input and output to remove the DC bias voltage
from LM324 datasheet:
Large Output Voltage Swing 0V to V+ − 1.5V
so you can get the ground but only 3.5V max with +5v supply. over this value the signal is deformed