OK, if you want to descend into sub-directories as well as working in the current directory, here's the command for you:
find . -type f -mtime +14 -printf "%Cw %p\n" | grep -v ^0 | cut -c3- | xargs rm -f
Please backup before doing this - I take no responsibility if it deletes the wrong files because I might have mis-interpreted your needs or made a mistake.
It is probably a good idea to run it without the "| xargs rm -f" on the end first and verifiy that the files it lists are indeed the ones you want to delete, and only the ones you want to delete. i.e.
find . -type f -mtime +14 -printf "%Cw %p\n" | grep -v ^0 | cut -c3-
OK, now for an explanation.
The -printf option to find can be used to print more information that the default (which is just to print the file path & name. In this case I used the format string "%Cw %p\n". Please look at the find manual page and find %C. If you read this section of the page, you should be able to see that "%Cw" means the day of week number (0-6) the file was last modified. (0 is Sunday). I could also have used %Ca which would print the day of week like "Sun", "Mon" and so on, but this is locale dependent, so it would not work on a machine with German language settings for example.
The next bit, "%p\n" just means the file path & name with a new line character after it.
The "-mtime +14" means to print only files older than 14 days since the last modification.
The "-type f" means to only print files.
The "." as the first option to find means "start in the current directory".
In you run the find command without the following pipeline, you will see something like this:
The number is the weekday of modification of the file (0=Sun, 3=Wed, 6=Sat), then the file name in question.
We do not want to delete files which were modified on a Sunday, so we exclude the lines beginning with 0 with the next part of the pipeline:
If the example output of the find command above is what you get, after the grep part, it will look like
The next part of the pipeline:
...prints only characters from column 3 onwards - it cuts off the day of week and the space. We now have just a list of files which we want to remove:
This is the input to xargs which calls the specified command (rm -f) for groups of strings read from standard input - i.e. remove the listed files.
I hope that is clear. If you have further questions about it, feel free to ask.