Deor 1 be wurman: Weland the smith is a well-known figure in Germanic mythology, but no story survives that explains this reference to a hard time he had with worms (snakes? dragons?).
Deor 5 hine . . . legde: traditionally, "hine" is taken as the object of "on", "nede" as accusative plural of "nied" ("necessity" etc.), here with the specific meaning "fetters" and in apposition to "swoncre seonobende", but this sense of "nied" appears to be otherwise unknown and other grammars are certainly possible: "nede" may stand alone as an instrumental dative, "by compulsion," or it may be an accusative object, "swoncre seonobende" then being an instrumental dative: "laid compulsion on him with a supple sinew-bond".
Deor 6 swoncre seonobende: in the Volundarkvitha, Weland is hamstrung by Nithhad (that is, the ligaments at the back of his knees are cut); attempts to read this phrase in Deor as a reference to such hamstringing seem forced. More likely, the English poet knew a different version of the story in which Weland was incapacitated by being tied up, perhaps using his own ligaments.
Deor 7 Þæs ofereode, þisses swa mæg: No similar instances of "ofergan" with genitive seem to be recorded, a fact that has caused much speculation. Without attempting to reproduce the entire argument, the current dominant position is that the verbs here are impersonal and the genitives (though not exampled so elsewhere) "of respect." The general meaning would then be, "It passed over with respect to that; it may also (pass over) with respect to this." See Klinck 160 for such an account and some background on the discussion. Mitchell (Old English Syntax 587–88) would class the genitive instances here as adverbial "of point of time from which" and translate "It passed over from that; it can from this." Another possibility, to my knowledge unexplored, is that "þæs" and "þisses" are objects, "ofergan" taking the genitive because its sense here includes the notion of "gaining" or of "possessing and ruling" (Mitchell, Syntax 449): "(He) conquered that; (I) may also (conquer) this."
Deor 14 Mæðhilde: The characters Mæðhild and Geat and their story are otherwise unknown in Germanic legend, but similar names in a late Scandinavian ballad allow us to conclude that they are lovers subject to some cruel fate here.
Deor 26 þæs . . . wære: "that his ("that one's") kingdom were overcome." MS reads "þæs cynerices ofercumen wære" again a possible genitive of respect (so Klinck and others), though Mitchell (loc. cit.) argues against any such thing as a genitive of respect existing in Old English and suggests that the genitive here modifies implicit "wean" carried over from the previous line.
Deor 30 earfoða (Connybeare, perhaps as a mistranscription): MS reads "earfoda".