Then, couldn't it in theory absorb the focusing properties of the different wand wood?
It seems unlikely. First of all, a wand is formed from two main components: the wand and the core. There isn't a whole lot known about the process of making wands from the books, but I suspect there's more to it than simply putting the core inside the wood. Simply cutting through some wood doesn't seem like it would do anything at all; the properties that a wand exhibits when made from a particular wood might only be present when it is in fact a wand. In other words, there may be nothing particularly special about the wood of an elder tree until it's used to create a wand.
Then there's the fact that a large part of the tension and violence between goblins and wizards stems from the latter's refusal to allow goblins to carry wands and to share the secrets of wandlore with them. If goblins could "simply" craft a sword like Godric Gryffindor's, take a few swipes through some wand wood, and get all of the benefits, that wouldn't be an issue.
For example the killing power of basilisk venom and the healing power of phoenix tears, how would that end up?
The sword - while a powerful magical artefact - is still at its core a sword; it's a weapon intended for killing. Basilisk venom improves its ability to serve its purpose, the healing power of phoenix tears doesn't (a sword that instantly heals the thing you're trying to kill wouldn't be very useful, and the sword itself doesn't have any need to be able to heal). Pure speculation, but I doubt it would imbibe the power of phoenix tears just because it wouldn't make it stronger in the strictest sense.
Other than those two specific examples, there are no stated limits to its ability to imbibe that which strengthens it. Given that it's already a fairly powerful artefact, there may be a limited number of things that it would even consider to strengthen it. That number may further decrease as it is strengthened by more substances - once it's absorbed basilisk venom it probably wouldn't have any need to absorb any other, less potent, venom since it already has the best available.