We describe a 22-year survey for variable and transient radio sources,
performed with archival images taken with the Molonglo Observatory Synthesis
Telescope (MOST). This survey covers 2775 \unit{deg^2} of the sky south of
δ<−30° at an observing frequency of 843 MHz, an angular
resolution of 45 \times 45 \csc | \delta| \unit{arcsec^2} and a sensitivity
of 5 \sigma \geq 14 \unit{mJy beam^{-1}}. We describe a technique to
compensate for image gain error, along with statistical techniques to check and
classify variability in a population of light curves, with applicability to any
image-based radio variability survey. Among radio light curves for almost 30000
sources, we present 53 highly variable sources and 15 transient sources. Only 3
of the transient sources, and none of the variable sources have been previously
identified as transient or variable. Many of our variable sources are suspected
scintillating Active Galactic Nuclei. We have identified three variable sources
and one transient source that are likely to be associated with star forming
galaxies at z≃0.05, but whose implied luminosity is higher than the
most luminous known radio supernova (SN1979C) by an order of magnitude. We also
find a class of variable and transient source with no optical counterparts.Comment: Accepted for publication in MNRAS. 34 pages, 30 figures, 7 table