What I found by doing a little online research, was that the unusual (or "weird" - I think I said) volcanic rocks on Mauna Kea are 1) the Hamakua Volcanics, composed of basaltic rocks called picrites, ankaramites, and alkalic and tholeiitic basalts, and 2) the Laupahoehoe Volcanics, composed of hawaiites, mugearites, and benmoreites (Kennedy et al, 1991 and Wolfe et al, 1997 - see below). Not all the rock types above, like picrites, are unusual to Mauna Kea; some can be found on the younger volcanoes of Hawaii.
Mauna Kea is essentially a late-stage basaltic shield volcano, which is what Mauna Loa and Kilauea (along with Pu'u O'o) will eventually grow up to be when they get older. Mauna Kea's end stage Hamakua and Laupahoehoe Volcanics essentially indicate that Mauna Kea is just about done, and is in the post-shield stage of its evolution, although it is still considered dormant rather than extinct, and more eruptions of the end-stage basaltic to andesitic flows would not be unheard of nor totally unexpected (Hawaii CVO site).
As for what these strange or unusual mostly basaltic rocks are, here is the best description I could find, and it approximates what I remember, though may not be 100% precise:
Basalt with extra Na+K = Hawaiite
Basaltic andesite with extra Na+K = Mugearite
Andesite with extra Na+K = Benmoreite
Dacite with extra Na+K = Trachyte
Mugearite or Benmoreite with LOTS of extra Na+K = Phonolite
A Few References and Links:
Kennedy, A. K., Kwon, S.-T., Frey, F. A., West, H. B., 1991, The isotopic composition of postshield lavas from Mauna Kea volcano, Hawaii: Earth and Planetary Science Letters, Volume 103, Issue 1-4, p. 339-353. [Abstract here.]
Wolfe, E. W., Wise, W. S., Dalrymple, G. B., 1997, The geology and petrology of Mauna Kea Volcano, Hawaii; a study of postshield volcanism: U.S. Geol. Survey Prof. Paper 1557, 129 p. [Abstract here.]
On Climbing Mauna Kea
On the Geochemistry of Hawaii Volcanic Rocks
On the Laupahoehoe Volcanics
Wikipedia on Mauna Kea