60. If a particular institution is responsible for overseeing compliance with existing rules against abuse of state resources, what powers is it granted?

In relation to general elections - 

"The Head of the Central Elections Committee of the Knesset may, after giving the person concerned an opportunity to present his arguments before him, issue an order preventing the commission of an offense under this Law."

Source: Article 17b(a), Knesset Elections Law (Propaganda Methods), 1959.

In relation to primaries -

"a) No use shall be made in connection with propaganda for primaries in the money or tangible or intangible assets of an audited body as defined in paragraphs (1) to (4) and (9) of the State Comptroller Law, or of a corporation which the Government or a local authority participates in its management or capital... b) The Head of the Central Elections Committee of the Knesset may, after giving the candidate or the person to whom the order is directed to him an opportunity to present his arguments before him, to issue an order preventing the commission of an offense under subsection (a) or its continuation."

Source: Article 28y3(a-b), Parties Law, 1992.

to issue an order preventing the commission of an offense  or its continuation.