A quick search only yields this for MD5: http://code.kx.com/q/ref/strings/#md5
Are there any other ways to implement SHA1/SHA256 without writing it yourself?
There is nothing inbuilt in kdb for that. You need to use external libraries and write an extension (for ex in C) to use that.
Below link has implementation to use OpenSSL library (which has functions for SHA*) in KDB.
https://github.com/johnanthonyludlow/kdb/tree/master/QCrypt
Pdf in that link explains how to use that.