Ultimately, everything in this answer is going to be at least somewhat speculative; Book of Exalted Deeds does not address the question of grafts at all. Reasonably, some will feel that this is rules-lawyering and abusing loopholes in a holy vow and that’s just not how things work—and they may well be right, since both Book of Exalted Deeds as well as external developer commentary suggests that, basically, if you have to ask, the answer is no.
So just, ya know, fair warning: if you are asking “should I take Vow of Poverty?” the answer is no.
A creature with grafts could take Vow of Poverty and (probably) keep them
Upon taking the vow, a creature must donate all of their worldly possessions to charity. But an already-extant graft isn’t a “possession” per se, it’s a body part and a creature should no more have to remove a graft than they have to remove an arm. This probably does necessarily mean waiting to take the vow until you have managed to procure some grafts, which means missing out on bonus feats—but then, there are very few good exalted feats anyway, and Vow of Poverty gives more than enough to get them all anyway.
A creature could not have a graft surgically applied to them after vowing
This is pretty straightforward: applying a graft costs money: even if a friend is doing it for you, they need to use expensive material that could be donated to charity. The Vow of Poverty thus demands that they are donated to charity, and not doing so and allowing them to be used for your benefit is a violation of the vow.
A creature with Vow of Poverty can get a graft magically...
...or, at least, can so long as they can navigate the alignment conflicts with that. Fiends of corruption and sibriexes (an obyrith, which is a type of demon) from Fiend Folio, as well as the aptly-named demonic graft machine artifact from Book of Vile Darkness, have the ability to magically apply grafts to creatures. This process costs them nothing, and so there is no part of it that could be donated to charity. So really, it does not break the vow at all.
The problem is that the vow is an exalted feat, which means maintaining exalted status, that is, better-than-Good status. Accepting gifts from fiends may well cost you your exalted status on its face, and thus kill the vow. But, if the DM agrees that circumstances permit an exalted creature to do this while staying exalted, this could get you a new graft after taking the Vow of Poverty.
A creature with Vow of Poverty who receives a graft against their will...
...is ambiguous in the extreme. The game is replete with examples of creatures failing requirements and losing features for things outside their control, which means the vow may very well be broken even if the creature who took it never intended to gain a graft. But it might instead be considered similar to the situation with magically gaining a graft, but without the alignment concerns. Which it is, we do not know because Book of Exalted Deeds does not really address it directly. Entirely up to the DM to sort out, probably on a case-by-case basis.
Magic of Eberron gives symbionts a treasure value. It doesn’t cover the symbionts in Fiend Folio but they would presumably be the same. This can make for an argument that you cannot have them. On the other hand, if Magic of Eberron is not in play, then nothing says they’re worth money, so you could maybe make an argument for keeping them, akin to an animal companion. But animal companions are a class feature; symbionts may be more similar to owning a regular horse—which a creature cannot do with Vow of Poverty.
Daelkyr half-bloods, also from Magic of Eberron, may be able to make a case for keeping their personal symbiont: it’s a free part of their racial features, and they suffer and die without it.