The influence of uniaxial and biaxial strains on electronic and transport properties of phosphorene nanoribbons (PNRs) is investigated within the tight-binding Green's function theory by including an iterative procedure. For this purpose, we use tensile and compressive strains and employ the electronic band structure, effective mass and current-voltage curve, to explore the transport mechanism of PNR devices. Our results based on the band structure show that pseudogap in zigzag PNR (zPNR) is tunable under the strains. Hence, the tunneling transmission is controllable between two edge states of zPNRs. Obviously, we observe that the compressive strains can disturb the electron distributions leading to the induced charge polarization in armchair PNRs (aPNR). Also, in some particular cases there is massive-massless Dirac fermion transition in aPNRs. We found that the p-type zPNR devices can be designed under the compressive strains and the n-type aPNR devices can be modulated under the tensile strains. Our results show that the strains can be used as a way to control and improve the negative differential resistance phenomena in zPNRs. In aPNRs the current and threshold voltage under a finite bias can be changed several times with the uniaxial and biaxial strains. Thus, PNRs can be utilized for the development of flexible electronic and field effect transistor nanodevices.