The injection of polymer solutions into an oil basin can lead to enhanced oil recovery (EOR) by increasing the microscopic sweep of the reservoir, improving the water-oil motility ratio, and thus leading to greater yield from oil fields. In this contribution, we characterize both shear and extensional rheological response of aqueous solutions of partially hydrolyzed polyacrylamide (HPAM), the most commonly used polymer for EOR, for velocity gradients in both the flow direction (extensional) and perpendicular to flow (shear) arise in EOR applications. As HPAM is a charged polymer, to better emulate the environment in oil basins, the rheological response was investigated in presence of salt, sodium chloride, and calcium chloride, with concentrations 3.7x10(-4)-1.5M, as a function of polymer molecular weight (2-10 million g/mol) and concentration (0.005-0.3wt%). The extensional relaxation times and extensional viscosity are measured using dripping-onto-substrate (DoS) rheometry protocols, and a commercial shear rheometer was utilized for characterizing the shear rheology response. The polyelectrolyte solutions formed by HPAM exhibit shear thinning in steady shear, but show strain hardening in response to extensional flow. Even though an increase in monovalent salt concentration leads to a decrease in both shear viscosity and extensional relaxation times, an increase in divalent salt concentration leads to an increase in extensional viscosity and relaxation time, implying that ion coordination can play a role in the presence of multivalent ions.