Welcome to the forum.
This ARTICLE will give you some background on AVI files (and many others), and tell you how to get all the necessary information inside their "wrappers."
Please give us the info on those AVI files. It is likely that you will wish to convert them to DV-AVI Type II files w/ 48KHz 16-bit PCM/WAV Audio, which will edit well and smoothly.
I agree with Hunt. Many AVI files (such as those from still cameras or pocket "webbie" camcorders) use unusual codecs that do not work well in Premiere Elements.
FLVs are not a supported source format.
As has been pointed out by Hunt and Steve Grisetti, all files with an .avi file extension are not created equal. And, DV AVI is the native format of the Premiere Elements Timeline. That AVI wrapper format can have numerous video/audio codec (compression) possibilities contained in that AVI wrapper. What kind of .avi do you have? If you are not sure, you could use the gspot software mentioned in Hunt's link or, if you give the brand and model of the camcorder from which it came, we can look it up.
As for use of those Flash files (.swf, .flv, and .f4v) in Premiere Elements 7, that .swf is the only one that you can import. Have you tried file conversion on the .flv and .f4v? That Moyea plug for Premiere works for Premiere Elements 4, but not 7, and probably not for version 8. In my preliminary work with Premiere Elements 8, it looks like you can now import .f4v as well as .swf, but still no .flv.
That Moyea plug for Premiere works for Premiere Elements 4, but not 7, and probably not for version 8.
Yes, this was a big disappointment for many. It was the same with PrPro. Moyea worked fine in CS2 & CS3, but not in any flavor of CS4. Too bad.
Now, they do have a stand-alone converter, that gets good reviews, but that would be so much easier, if it could be a plug-in. This would be something to explore.
It is good to know that PrE 8 is getting more Flash support too.
One thing that we must keep in mind is that FLV is basically a delivery format and is not really meant to be edited. Much of this material comes FROM YouTube, where it has already been edited and then Exported for delivery. This is just like DivX and Xvid - delivery only.