Are you sure you have the right IC? THe LM324 is a quad, single supply op-amp. It can be used for a battery low and an overload detector, but not so easily for an inverter.
1) For a battery low, you would configure it as a comparator with hysteresis. the reference voltage would be equal to the battery low point and can be adjustable with a pot. You need a reasonably good DC reference voltage. THis can be from a zener diode, a TL431, or a bandgap reference IC. The comparator will use 1/4th of the IC (1 of 4 op-amps), leaving 3 leftover. The comparator circuit here will need to have the op-amp inputs arranged so that it trips on a low-going input. Since the LM324 is an op-amp and not a comparator IC, the op-amp output needs to connect to a MOSFET (2N7000 or similar) or a bipolar (2N2222 or 2N29072N2907) to allow the circuit's output to be a switch instead of a linear output voltage. If using a bipolar, a resistor will be needed between the op-amp output and the base. For a mosfet, this is still recommended. but not essential.
2) For the overload detector, you need your inverter's output load current sensed by a current transformer (CT). The CT would be put thru a diode bridge to rectify the AC current, then needs a resistor across the bridge DC output with the minus side of the bridge to Return (GND). Now, the circuit is almost identical to the battery low detector as it will use another 1/4th of the LM324 as a comparator, except the op-amp's input terminal polarity is reversed so that the comparator will trip on a high-going input instead of a low-going input. Since a comparator circuit's output is a switch and not a linear output voltage, again, a mosfet or bipolar transistor as mentioned above will be needed. This is typically in an open-collector or open-drain configuration.
