When I try to import a movie .avi or .jpg, I can't select anything. All files are grayed out.
To begin with, JPG giles cannot be "imported" to either an Event or a Project. They can be dragged and dropped from the photo browser to a Project or (as you noted) they can be dragged and dropped directly from the Finder to a Project. As to AVI files, you will have to be more specific. AVI is a file container in which various forms of compressed audio and video content can be placed. Basically, if either the audio or the video data is compressed in a format that iMovie '08 cannot edit, the application will not let you import the file. Video formats like DV, AIC, M-JPEG, Photo-JPEG, MPEG-4, and H.264 can be edited. Audio formats like Uncompressed, DV, AIFF, AAC, various "Integer" compression schemes, etc. can be edited. In addition, AVI files containing proprietary compression formats like WMV, DivX, 3ivX, Microsoft MPEG-4 variations, etc. cannot be edited because third-party QT components cannot be accessed from within iMovie '08.
Why? Isn't this a movie making application?
No. Actually it is a video editing application. Like many, you make the mistake of lumping all forms of video together as if they were all the same. As far as QT is concerned, some forms of video are "playback" only. The can be played but not converted to other compression formats nor edited. Other formats can be played as they and cannot be edited but can be converted to an "edit" compatible formats that can be used in iMovie '08. The last group is composed of "edit" compatible compression formats which can be edited, played, and/or converted as they are. Just as you cannot play a DVD on a CD player, you cannot import files which are not compatible with editing in the QT structure.
And I can't important any movies? What am I doing wrong?
You are not converting the files to an edit compatible compression format. If the files play normally in QT or QT based applications, then you may well be able to convert them to an editable format.