Nodal analysis -> transfer function -> step response
Nodal analysis is based on Kirchoff's Current Laws (KCL), meaning that the sum of all currents will need to sum up to exactly \$0\$.

The issue in your equations is related to the fact that outputs of opamps are voltage sources, and they will also inject a current in a node. So, for example in node D you would get instead

$$0 = (v_A - v_D)\cdot sC_3 + (v_B - v_D)\frac{1}{R_2} + i_{oa1}$$

As is, this circuit becomes unsolvable as we just inserted another unknown. In order to make the circuit solvable again, the added unknown current will need to be fixed by another (linearly independent) equation, in our case this is the virtual short-circuiting of the inputs;

$$v_B = 0$$

This problem has 6 unknowns (A through E and \$v_0\$), so you will need 6 KCL equations. There are 3 opamp outputs, so you would (when not simplifying the system of equations) ultimately have 3 extra virtual short-circuit equations and output current unknowns totaling to 9 equations and unknowns.