Is there a particular term for the abbreviated language used in headlines (the removal of at least articles and conjunctions)?
Mårdh (1980) refers to this type of language as "headlinese". (Mårdh, Ingrid. 1980. Headlinese: On the grammar of English front page headlines. Malmö: CWK Gleerup.) See also this Wikipedia page.
A particularly bewildering headline can be referred to as a crash blossom. This term was taken from the headline: "Violinist linked to JAL crash blossoms".