If I swear something on the River Styx, is it possible to take it back?
TLDR: No. It was the one oath that was binding, but only used by heavenly beings.
"[Hypnos (Hypnus), the god of sleep, insists Hera seal her pledge to him by an oath on the Styx :] ‘Come then! Swear it to me on Styx' ineluctable water. With one hand take hold of the prospering earth, with the other take hold of the shining salt sea, so that all the undergods who gather about Kronos may be witnesses to us.’"
If Hera pledges to Hypnos, and Hypnos insists that it is not enough, then suggests a River Styx oath, then I would say that means it's not able to be taken back.
Also, it was the strongest oath you could make!
"And Leto sware the great oath of the gods : ‘Now hear this, Gaia (Gaea, Earth) and wide Ouranos (Uranus, Heaven) above, and dropping water of Styx, this is the stongest and most awful oath for the blessed gods.’"
Virgil says that it is the one dreadful and binding oath
"This I [Jove, Zeus] swear by the source of the inexorable river, Styx--the one dreadful and binding oath for us heaven-dwellers."
Also note that it says heaven dwellers. This means that lesser mortals can't swear on the River Styx. That does not mean that they cannot witness it, as we see in the story of Semele, or Phaethon
"The girl [Semele]. unwittingly, asked of Jove [Zeus] a boon unnamed. ‘Choose what you will’, the god replied, `‘There's nothing I'll refuse; and should you doubt, the Power of rushing Stygia shall be my witness, the deity whom all gods hold in awe’ [and she asked him to appear before her in his full glory, a request which Zeus could not now refuse and which doomed the girl]."
"[Helios (Helius, the Sun) swears an oath to his son Phaethon:] ‘Well you deserve to be my son’, he said, ‘Truly your mother named your lineage; and to dispel all doubt, ask what you will that I may satisfy your heart's desire; and that dark marsh [the river Styx] by which the gods make oath, though to my eyes unknown, shall seal my troth.’ He scarce had ended when the boy declared his wish - his father's chariot for one day with licence to control the soaring steeds . . . [Helios to Phaethon:] ‘By Stygia I swore and I shall not refuse, whate'er your choice: but oh! more wisely choose!’ So Sol [Helios] warned."