Drelnza, at the doors to the Nexus, holding Daoud's Wondrous Lanthorn aloft, as portrayed by Jeff Easley. Source: The Vampire Daughter Print, from Art of the Genre.
Here is the relevant section on vampires from OD&D vol. 2:
These monsters are properly of the “Undead” class rather than Lycanthropes. If they are exposed to direct rays of sunlight, immersed in running water, or impaled through the heart with a wooden stake they are killed; otherwise they can be hit only as Spectres, but such hits do not kill them but only force them to assume gaseous form if they lose all hit points. Vampires drain two life energy levels as do Spectres when they hit an opponent in combat. They regenerate during combat as do Trolls, but they do so immediately upon being hit at the rate of three hit points per turn. Vampires can command help by calling to them from 10 to 100 rats or bats or from 3 to 18 wolves. They can polymorph themselves into either a huge bat or into a gaseous form, doing either at will. They Charm men-types merely by looking into their eyes (treat as a Charm Person spell with a minus 2 for the object’s saving throw against magic). Vampires cannot abide the smell of garlic, the face of a mirror, or the sight of a cross. They will fall back from these if strongly presented. They must always return to a coffin whose bottom is covered with soil from their native land during the daylight hours. Men-types killed by Vampires become Vampires under the control of the one who made them.
The Greyhawk supplement provides additional details:
All Vampires are affected by the cross, despite any former religious background, as it is sovereign against them. It must be noted, however, that the Vampire will not flee from such a symbol but merely try to position itself so that the cross (or whatever) no longer interposes its powers between the Vampire and its intended prey. There are other similar symbols of power versus vampiric creatures, and they can be introduced if the referee so desires. Vampires from the region of the Middle East are invisible, but they are not able to Charm.
The AD&D 1e Monster Manual further specifies "These creatures must rest in a coffin or similar receptacle* during hours of sunlight unless far beneath the surface of the ground" and that "Vampires have 18/76 strength."
*the original version of "The Lost Caverns of Tsojconth" makes no mention of a coffin. I've therefore contemplated the idea of regarding the Core of the Nexus as Drelnza's "coffin" (the walls are described as panels of polished wood), which has scary implications
"Vampires in the Dungeon" by Clayton J. Miner, from The Dragon #17 (August, 1978) gives some helpful tips on running OD&D vampires.
Vampires from the Middle East, mentioned above, are identified as "Ekimmu" from Assyria in "Varieties of Vampires" by R.P. Smith, from The Dragon #25 (May, 1979), another casual reference to the OD&D Game World as a version of our own world.
Finally, the article "Good Evening" by Lenard Lakofka, from The Dragon #30 (October, 1979) provides some useful additional information, such as rules for meeting a vampire's gaze, as well as stats for the various creatures summoned:
BATS: 90% of the time they should be the mundane sort that “hang around” in caves, bell towers, etc. They have 1–4 hit points, are Armor Class 7 (due to size and speed), move 12” (but usually flurry about figures when a Vampire summons them), do “inadvertent” damage of 1 point 50% of the time — if and only if at least 5 are swarming around a single figure and the Armor Class of the victim indicates a hit. Swarms reduce the ability “to hit” by 3 points. 10% of the time, however, 1 Vampire Bat per 10 bats (round down) may appear. It is 1 hit die A.C. 8, moves slower, 9”, and does 1 point of damage per hit. In addition, if it does it drains 1–4 points of blood just as a Stirge does but then flies away after 8 points are drained.
RATS: 90% of the time they should be the mundane sort that scurries about in dungeons, though they will always be especially large rats. 1–4 hit points, A.C. 8, bite causes 1 point of damage (no change of disease). But 10% of the time (and only in especially deep dungeons) Giant Sumatran Rats will appear, as per the Monster Manual. The quantity of these Giant Rats is 7–70 and not 10–100.
WOLVES: Their type should be a function of the climate. If in polar regions, Winter Wolves should appear, but only 2–7 would come. In other areas the chance of the normal wolf is 70% for the full 3–18 in number (see the Monster Manual); however, 30% of the time 2-14 (1d6 + 1d8) Dire Wolves will appear.