Effects of steady elongational flow on orientational phase transitions in systems of uniaxial, elongated particles with dipole moments are considered. The Onsager model is used with mean-field dipole-dipole and excluded-volume quadrupole interactions, combined with quadrupole effects introduced by elongational flow. Self-consistent, equilibrium orientation distribution of dipole particles, equilibrium thermodynamic properties and phase transitions are controlled by three dimensionless parameters related to dipole-dipole interactions, excluded-volume effects and intensity of the flow field. Dipole and axial order parameters, phase equilibria, and phase instability points are discussed in the space of dipole and quadrupole interaction parameters. Apolar-to-polar phase transitions, as well as transitions between individual apolar phases are affected significantly by coupling between excluded-volume effects and elongational flow. Three ranges of flow intensity inducing different phase behaviour are discussed. In a the weak flow range, a single polar phase and two different apolar phases are predicted. Phase diagram shows a triple point and three equilibrium fines for different pairs of phases. In the medium flow range, the triple point disappears and phase diagram reduces to two phases, apolar and polar, with a single line of coexistence. The first-order apolar-to-polar phase transition appears at relatively low values of the quadrupole interaction parameter, while at higher values of the parameter, second-order transition takes place. The first-order ferroelectric transition, as well as the coexistence of apolar and polar phases, disappear at a critical flow intensity separating the range of medium and strong flow. Within the strong flow range, the ferroelectric transition is second-order in the entire range of quadrupole interactions. Dipole-dipole interactions, critical for the ferroelectric transition, are significantly reduced by flow potential, especially at stronger excluded-volume interactions. A critical flow intensity has been found at which ferroelectric transition is stabilised solely by the elongational flow. Above the critical flow intensity, the system exhibits single-phase behaviour with stable polar order. No elongational flow is capable to induce ferroelectric phase transition in systems with dipole interaction parameter lower than unity.