Those weird outputs are terminal control commands, which are a remainder from the old (VT100) terminals. These codes move the cursor around, change text colors, and are used for some kind of formatting as good as it can get on the old terminals.
If you want to get rid of these codes, you can select in Putty to only log printable commands:

For most purposes that is easier. If you log to files and have large outputs, I think that you already found the command: "no page" which disables the pagination (-- MORE --, next page: Space, next line: Enter, quit: Control-C) thus need to press space all the time.