The voltage rating and power factor (PF) should also be known. If the PF is not none, you can get it by applying the rated voltage and measuring all of current and P and Q, or you can measure the power factor also. If the load is a motor, you need to do the two well-known tests that are called the open circuit and short circuit tests.
If not motor, then, from the measurements above, you can obtain R and L.
If there is difficulty to build the test circuit in the lab, you can simulate it in a suitable simulation software. MATLAB/SIMULINK would be useful.
Active power(P)=W=VICos(phi)=VI=I(sqr)R, as p.f angle is zero for resistive load. Hence if W and I=W/V is known R could be obtained easily.
Reactive power(Q)=VISin(phi), L or LC with higher L effect p.f would be lagging(.8 lag normally for power system).
C or LC with higher C effect p.f would be leading, Total power(VA)=P +/- j(Q).
V=I.Z, Z=V/I, Z=R +/- jX, hence by knowing Z and R, X of system could be obtained, and X=2(pai)fL, for lagging p.f, L could be obtained. X=1/2(pai)f.C, hence C could be obtained for circuit with leading p.f.