If a time-series has odd number of samples does it have no energy at Nyquist frequency?
No, that's not what it means. You just don't get a frequency bin at Nyquist if the DFT length is odd. If you want you can always append one or more zeros to the time domain sequence such that the total length becomes even.
If you're just interested in the energy at Nyquist, you could also simply compute
$$E_{Nyq}=\left|\sum_{n=0}^{N-1}x[n](-1)^n\right|^2\tag{1}$$
where $N$ is the length of the sequence, no matter if it's even or odd.