A two-year corruption and international money-laundering investigation stretching from the Jersey Shore to Brooklyn to Israel and Switzerland culminated in charges against 44 people on Thursday, including three New Jersey mayors, two state assemblymen and five rabbis, the authorities said.

The case began with bank fraud charges against a member of an insular Syrian Jewish enclave centered in a seaside town. But when that man became a federal informant and posed as a crooked real estate developer offering cash bribes to obtain government approvals, it mushroomed into a political scandal that could rival any of the most explosive and sleazy episodes in…