Where You Stand
Unfortunately, it seems as if you've already tacitly agreed to accepting these messages (I assume that if you had ignored or blocked from the first message, they wouldn't still be sent to you). That means you have already set an expectation of behavior from your manager saying, "I am willing to do this".
This puts you in a sticky spot where just blocking him or ignoring the messages runs the risk of really pissing off your manager because he may assume there is a tacit agreement that this behavior is okay, and yet you are suddenly changing the rules without so much as a hint. It's passive aggressive, and may not go over well, so I would discourage it.
How Do You Feel?
Clearly something about this is bothering you. But which aspect is it? Do you not like getting texts in the middle of the night? Not like working without getting paid? Not like using your mobile phone?
You have to sort that out first. Which things are absolute no-gos, and which ones are you okay with, and under what circumstances/conditions?
For instance, if you don't like getting texts in the middle of the night, and you don't like getting them to your personal phone, but don't mind doing a little "on-call work" if you get paid for it and it isn't through your personal phone, then you can figure out what you want:
- Overtime pay for on-call work
- Company phone
- On-call hours of X o'clock to Y o'clock
How To Get What You Want
I would recommend not being confrontational about it. Yes, these may be unreasonable requests, but the guy is your boss, and if you know what you want you are far more likely to get it taking a positive forward-looking approach.
- Check your contract to see your legal obligations to the company (does your job description actually include any provision for occasional overtime or anything else this may fall in to?)
- Check with your coworkers to see what the company actually expects (does everyone else in your office do the same thing?)
- Quickly summarize the amount of time it would take to do what is being asked (are these short 5-minute tasks that can be tackled in a couple minutes, or do they require actual work?)
Once you know what the company expects, and what they are realistically asking, you are in a proper situation to negotiate. For instance, if your other coworkers are doing the same thing, then telling your boss, "I absolutely refuse" is not going to go over well (like it or not, "but everyone else is willing to do it" is a really strong argument). If they aren't, then you know that either (a) they may be able to let you know how they dealt with the situation before, or (b) the boss trusts you for a task he finds important enough to contact you at any time about and you have a lot more bargaining power.
Soften Him Up
Based on your answer to the How You Feel section, you can now have a nice conversation with your boss. Start with something that will make him happy, as it will put him in a better mood and get you a better negotiating position. For instance, "I am really flattered that you trust me enough to ask for my advice when something goes wrong, I really appreciate that you have that much confidence in my work." If he knows what he is asking is a little much, he'll appreciate you turning it in to a positive, and if he is socially dense and thinks that what he's been doing is okay, you're hinting that he finds you important which can't hurt.
Acknowledge His Concern
You want to get him agreeing with you and start off with something he won't disagree with, something like, "Since problems can happen at any time, we really should find a good way to share the burden of problem-solving outside of work hours." The point is that you're making him say "Yes" right from the start which will make him feel more willing to go along with what comes next.
Based on what you actually want/your situation you should edit this as needed, but something like, "If we had someone on-call a day a week, gave them a company phone so that the contact point was always the same, I think it would be a lot easier to get people to cooperate, especially if they get an extra day off a month to make up for the overtime." Or, "You know I'm happy to help any time I can, but there will be times when I can't respond immediately, is that okay? How should we work out invoicing the company for overtime payments?"
Basically, you want to give him a solution that will solve his problem, and couple it with a totally reasonable request (overtime pay, additional vacation) to make up for the added burden. You are saying, "Hey boss, I know this is important, so of course it's worth giving us something back for." Only in nicer terms.
Afterwards, let him talk. He may say, "Golly gee, I didn't think about the extra burden, I'll stop doing that", or he may say, "That's a great idea! I'll talk to payroll about the overtime payments!" The point is let him speak his mind, and if he gives an alternative suggestion that you can happily agree with, give him ownership of the idea and just work out a schedule for implementing it.
There are plenty of bosses in the world who don't care if the request is unreasonable, and won't appreciate you asking for just compensation. If this is the case, and you need the job, be prepared to suck it up and do on-call work. If you don't need the job, you may want to make sure your CV is updated.
While I'd love to say that there is a clearly defined line between "acceptable" and "unacceptable" in the employer-employee relationship, in my experience there isn't. You are on a continuum with all the other employees and potential employees in the world. If the economy takes a plunge, people willing to do horrid things are more plentiful, and employers get away with more. If the economy booms, you have pizza drivers getting $500 bonuses because it's impossible to get people in those positions. You should evaluate where you stand, where you are willing to compromise to ("not at all" is also an acceptable answer), and take the appropriate action to find that happy spot.
In no way am I advocating that this behavior by the manager is acceptable, or that anyone should feel the need to oblige their boss' every whim. Just figure out what's best for you and find the best way to get there.