Can the administration make transfers between budget functions during the year without seeking board approval?
Not if the district appropriated their budget by function, which is how most do it. If the budget appropriations were made at the function level, then any transfers between those functions have to be authorized by official resolution or ordinance of the governing body as specified in ORS 294.450.
294.450 Transfers of appropriations within fund or from one fund to another; appropriation of pass-through revenues. Subject to the provisions contained in the charter of any city or county or in any law relating to municipal corporations: (1) Except as provided in subsection (2) of this section, transfers of appropriations may be made within a given fund when authorized by official resolution or ordinance of the governing body. The resolution or ordinance shall state the need for the transfer, the purpose for the authorized expenditure and the amount of appropriation transferred. (2) Transfers of general operating contingency appropriations which in aggregate during a fiscal year or budget period exceed 15 percent of the total appropriations of the fund may be made only after adoption of a supplemental budget prepared for that purpose. All other transfers of general operating contingencies are subject to subsection (1) of this section.