Mono-layered h-BN and its derivatives are very important low-dimensional materials, which have been widely investigated so far. Here, we theoretically study the structural stability and magneto-electronic properties of oxygen (O) terminated zigzag-edged h-BN nanoribbons, especially focusing on strain tuning effects. The O dimerization at the B edge of the ribbon enhances the system stability greatly. A Poisson ratio of 0.2 and bearing a strain more than 20% can be reached. In the absence of strain, the O-terminated ribbon is a magnetic metal. However, the rich magnetic phase transitions among the non-magnetic metal, a spin gapless semiconductor, and a wide-gap half-metal can be realized continuously by applying strain in the ferromagnetic state. Thus, based on such a material feature, we can design a magnetic switch device which can work between the magnetic and non-magnetic states by strain modification. Also shown is that the magnetism stability can be enhanced to the level at room temperature upon strain, and the massless Dirac-fermion behavior for the β-spin state can be clearly detected in the spin gapless semiconductor phase under appropriate strains.