Corrupted - this is a very interesting word. Does the significance of this word suggest that there exists a way to achieve similar results using non-corrupted blood? If the fault with Oeden lies not with the Great One but with the initial humans (who may have not fully understood what they were doing) than could there not be a way to communicate without corruption?
The idea is, I think, that blood which has been touched by the Great Ones opens that person up to influence by the Great Ones. Here's the description from Arianna's Blood Vial:
"
A member of the old Healing Church would know that her blood is similar indeed, to precisely what was once forbidden."
What was once forbidden was the Old Blood- or, in other words, the original blood given to man by the Great Ones, or that which was found in the old labyrinths. We know this is the case because of what we see of Provost Willem's conversation with Laurence, founder of the Healing Church. "Fear the Old Blood" was Willem's adage, which Laurence disobeyed.
We know that this isn't the first time this has happened, either. There's a woman who shares many similarities, physically, to Arianna: Yharnam, the Pthumerian Queen, who is implied to be Mergo's mother.
From the Blood Rapture rune: "
This rune resonates with servants of the Queen, carrier of the Child of Blood, who yearn for their Queen's blood with little hope of requitement. For them, they find solace in "Blood Rapture," that serves as a surrogate for their desires."
In other words, it seems that some people in this world have a natural tie to the Great Ones through their blood. They're born with some special quality that makes their blood extremely similar to the gift of the Great Ones- this in turn allows the Great Ones to influence them and to instill them with children, among other things.
I'm sure we could potentially communicate with Oedon without blood as a medium, but it'd probably mean getting one of the Mensis head-cage-antennas and raising insight as high as it'll go. Even then, he might just fry our brains.
Edit: I forgot to mention. The word 'corrupt' is associated with the Vilebloods, who were persecuted for their use of 'corrupted' blood taken from Byrgenwerth. Notably, their queen has the ability to regenerate infinitely, if her remains are brought to an altar that is blessed by the Great Ones. So maybe there's something to that?