Apparently there are 2 electron self-energy graphs possible. The first, the more "familiar", where the incoming electron at time $t_1$ splits up in a photon and an virtual electron. At $t_2>t_1$ the virtual photon joins the electron again. But the Feynman-propagator also allows $t_1>t_2$, where apparently the incoming electron hits a positron at $t_1$ which was created at time $t_2<t_1$. But for the creation of the electron-positron pair at $t_2$ the photon has to provide the positive energy at $t_2$ for the creation process, so this photon seems to be created at $t_1>t_2$, so the photon is apparently moving backward in time. The other possibility is of course apply Feynman's saying: Backward in time running particles with energy $E$ can be interpreted as forward in time running particles with $-E$ (assuming $E$ can have positive or negative sign in general). Therefore, it would be equivalent to say that for the electron self-energy diagram where $t_1>t_2$, at $t_2$ a photon is created with energy $-E$ ($E$ being the energy needed for the creation of the electron-positron pair) and then moving in time forward to $t_1$ to deliver this negative energy to destroy the (incoming) electron-(virtual) positron pair. Therefore I come to the conclusion that virtual photons can have negative energy in running in time forward or positive energy running in time backward.
What about real photons? I would be astonished about real negative energy photons. Or would the dispersion relation $\omega^2=k^2$ allow for negative frequencies (keeping in mind that these negative frequency solutions would again correspond to photons as anti-photons and photons are the same)?