"Im Hause" - "in the house" (location) -- dative
"In das Haus" - "into the house" (direction) -- accusative
In general, "in July" signifies a location in time, so you need the dative.
You could use the accusative for a stretch of time that starts before, but moves into the month:
"Ich werde bis in den Juli arbeiten". - "I am going to work into July" (don't know if this sounds good in English, but it should give you the idea).
EDIT: There are many expressions with time that all use the dative case:
"Im Juli, im Oktober. Im Sommer, im Winter. Am Morgen, am Mittag, am Abend, in der Nacht. Im nächsten Jahr. In der letzten Woche."
We just don't use the article in English - at least, I can't think of any context in which we would. E.g. "next year in July" and "in July of/in 1986" sound much more natural to me without the "the".
(German uses articles for months much more often than English does, which is why we have im; the hints for im can't be changed for certain contexts only, unfortunately.)