There was absolutely no possible way for the Japanese army (or for that matter, naval troops) to mount an invasion, due to a massive lack of not only available troops but also transport for those troops and a supply chain to keep them alive during a theoretical occupation. For one thing, an invasion of the main Hawaiian islands would have to be supplied across the central Pacific, past American-held outposts like Wake and Midway, or through the northern Pacific within range of long-range aircraft flying from the Aleutians. Not to mention that American submarines and commerce raiding ships would have a field day with supply convoys. (it's doubtful whether the Japanese could have even successfully held on to Midway, which is 1,000 miles closer to Japan than Oahu is.)

The Pearl Harbor attack was intended to cripple the American Pacific Fleet to buy Japan enough time to build a defensive perimeter in the western Pacific (it was coupled with attacks on western colonial possessions in the Philippines, Singapore, etc.). The theory was that the American fleet (eventually rebuilt, or transferred from the Atlantic) would be forced to arrack that strong defensive perimeter and would be first attrited, then be decisively defeated, after which the U.S. would sue for peace.

Edmunds and Peattie's Kaigun is a very readable primer on the topic: http://www.goodreads.com/book/show/1283911.Kaigun

Edit: /u/Prufrock451 makes a great point about there not being long-range aircraft in the Aleutians in 1941.