We begin our work by studying the most general class of oscillators, called ‘f-deformed oscillators’ or ‘f-oscillators’. We define the quadrature operator for the f-deformed algebra and hence obtain the deformed quadrature operator eigenstates. We derived a new set of polynomials and derived the deformed oscillator wavefunctions in terms of them. The position probability distribution for three different types of deformations are plotted, and each is compared with the corresponding non-deformed counterpart. The newly obtained quadrature operator eigenstates will be helpful for those who are working in the field of quantum state reconstruction and quantum information processing of deformed states.