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I am using qiskit to get some measurement results of observables similar to the Hamiltonian. Can someone provide the way how qiskit measures the Hamiltonian (Jordan-Wigner transformed) when using VQE? Or can they just provide the source code link.

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Measurements in a VQE (also in Qiskit) are performed as projective measurements. Have a look here for a related question in Physics SE. Citing from Nielsen and Chuang's book "Quantum Computation and Quantum Information":

A projective measurement is described by an observable, $M$, a Hermitian operator on the state space of the system being observed. The observable has a spectral decomposition, $$M = \sum_{m} mP_{m}$$ where $P_{m}$ is the projector onto the eigenspace of $M$ with eigenvalue $m$. The possible outcomes of the measurement correspond to the eigenvalues, $m$, of the observable. Upon measuring the state $|\psi\rangle$, the probability of getting result $m$ is $$p(m) = \langle\psi|P_{m}|\psi\rangle$$ Given that outcome $m$ occurred, the state of the quantum system immediately after the measurement is $$\frac{P_{m}|\psi\rangle}{\sqrt{p(m)}}$$

If you have access, also have a look at this paper.

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