Port scans. I'd expect IDS systems to be pretty effective at detecting most port scans. (It is a separate question whether it is useful to detect port scans.)
SQL scans. I'd expect IDS systems to be effective at detecting basic SQL injection attack attempts, e.g., where someone is poking at your server in a simple way. I would not expect them to be effective at detecting sophisticated SQL injection attacks. It is possible to build SQL injection exploits that evade detection by IDSs.
Credentials obtained. This is too broad; I don't know what path for obtaining credentials you had in mind, so I don't know how to answer it. If you are talking about attackers trying to get access to a web application by guessing usernames and passwords, I would not expect a network-based IDS to detect those attacks.
Installation of SSH. I don't know whether IDSs detect installation of SSH. I'm not clear on how they would distinguish an attacker who maliciously turns on a SSH server vs a sysadmin who turns on a SSH server for legitimate purposes. This seems like something you could test yourself easily.
Remote shell. I would not expect an IDS to be effective at detecting most remote shells. Perhaps sometimes, but once the attacker has the ability to run code on your machine, it is too easy for them to craft their own custom method for remote access that an IDS won't detect. It is possible that some common cases can be detected; I don't know, and don't have enough experience to know.
Other anomalous behavior. To the best of my knowledge, current network-based IDSs usually don't try to detect anomalies in general. Rather, it is more typical to have a signature of specific attack methods that have been observed in the wild. In other words, they try to detect known attacks, rather than unknown ones.
Detecting anomalies is quite challenging, and usually leads to many false positives. For instance, if you suddenly start seeing a lot more traffic somewhere, how do you distinguish the case where you just got Slashdotted (and this is legitimate traffic) from the case where you've had a security breach (and this is illegitimate traffic)? In the general case, it can get pretty tricky.
Detecting anomalies is quite challenging, and usually leads to many false positives. For instance, if you suddenly start seeing a lot more traffic somewhere, how do you distinguish the case where you just got Slashdotted (and this is legitimate traffic) from the case where you've had a security breach (and this is illegitimate traffic)? In the general case, it can get pretty tricky.