Fluid pressure and fluid velocity carry important information for cancer diagnosis, prognosis and treatment. Recent work has demonstrated that estimation of these parameters is theoretically possible using ultrasound poroelastography. However, accurate estimation of these parameters requires high quality axial and lateral strain estimates from noisy ultrasound radio frequency (RF) data. In this paper, we propose a filtering technique combining two efficient filters for removal of noise from strain images, i.e., Kalman and nonlinear complex diffusion filters (NCDF). Our proposed filter is based on a novel noise model, which takes into consideration both additive and amplitude modulation noise in the estimated strains. Using finite element and ultrasound simulations, we demonstrate that the proposed filtering technique can significantly improve image quality of lateral strain elastograms along with fluid pressure and velocity elastograms. Technical feasibility of the proposed method on an in vivo set of data is also demonstrated. Our results show that the CNRe of the lateral strain, fluid pressure and fluid velocity as estimated using the proposed technique is higher by at least 10.9%, 51.3% and 334.4% when compared to the results obtained using a Kalman filter only, by at least 8.9%, 27.6% and 219.5% when compared to the results obtained using a NCDF only and by at least 152.3%, 1278% and 742% when compared to the results obtained using a median filter only for all SNRs considered in this study.