Can I somehow convert .str streams to .avi format?
You should be able to convert PlayStation Video Streams directly to Audio Video Interleave Files (.str to .avi conversion), which can be done using several dedicated utilities.
Try using tools, such as PSXVideo or STR Converter, which claim they allow users to convert STR files to AVI video format.
A converter for PSX videos
A PlayStation movie converter
A universal all-purpose free media, audio & video converter