What you have described is not legal, in that, it is mandatory to have a strata committee, and for that committee to select a chairperson, a secretary and a treasurer. However, once it does this, the committee can delegate (nearly) all of its functions to the strata manager, assuming also that the strata manager’s contract with the Owners Corporation allows this.
Nevertheless the strata committee is legally liable for anything that the Owners Corporation does, and they can be sued (and held financially accountable) for any misbehavior that the Owners Corporation gets up to, or allows its strata manager to get away with.
If, as you say, the Owners Corporation at its AGM voted down the election of a strata committee, and is relying on its strata manager to do the necessary work to run the Owners Corporation, then this is at odds with strata law. So, you should check out the actual situation. Read the agenda and minutes of the building’s AGM, to determine what the situation actually is. Ask the strata manager to advise you of the makeup of the strata committee and its office holders.
And if there is no strata committee, you have 2 fairly easy choices – you should lodge a complaint with the Dept of Fair Trading, firstly that the Owners Corporation is not following strata law, and secondly with the licencing section of the Dept that the Strata Manager is not following strata law, and is representing a building without a legally sanctioned strata committee. The Strata Manager should have cancelled their management contract with the building, if the owners refused to follow the law.
However, there are many strata buildings where the owners do not wish to follow the law, and so the strata manager may step in and run things, and the Dept just assumes that this is the best of a bad set of options. This situation is likely to increase, once compulsory training of strata committees comes into force, which will discourage owners even more than now from being involved in building management. Strata law does not handle buildings where the owners refuse to manage the owners corporation, and owners are less likely than ever to want to get involved with the management of their buildings, which is a demanding and voluntary role.
If this situation really concerns you, discuss this with a strata lawyer. You would probably have a case to appoint a compulsory strata manager, which ironically, is the same situation you are currently in, although you and the other owners would have a say in who that manager would be.