If you were to regard your Owners Corporation as a private company, your Executive Committee as its Board of Directors, your Strata Manager as its paid Consultant, and yourself as a part owner of the company then that would be a good analogy.
So of course you’re entitled to view all the Owners Corporation’s records, including those relating to legal advice / actions, where in NSW and with reference to the Strata Schemes Management Act (SCMA), those must include “copies of correspondence received and sent by the owners corporation” [S104 (c)], “records served on the owners corporation by the strata managing agent relating to the exercise of functions by the agent” [S104 (g)], and “any other record or document in the custody or under the control of the owners corporation” [S108 (g)]. So surely those provisions will well and truly cover what you’re looking to peruse.
I don’t know on what basis you inspected the records on the occasion to which your post refers, but if your “Board” and your “Consultant” refuse to oblige on this occasion, I suggest that you put your request in writing to the Secretary of your Executive Committee and copy your Strata Manager, specifically referencing the records you want to inspect at the offices of the latter, and advise that your request is made pursuant to S108 of the NSW Strata Schemes Management Act.
On your side, there’s a prescribed fee of $30 for the first hour of your perusal pus $30/30 mins afterwards, both payable to your Owners Corporation, and whilst you can’t take any papers away from the Strata Manager’s offices you can take notes and make photocopies.
On your Strata Manager’s side, there’s a Penalty of $300 if the records held by them on behalf of your Owners Corporation (of which you’re a part owner remember) are incomplete or otherwise not in accordance with the SCMA.
If all else fails, it sounds to me like there are sufficient like-minded Owners to secure ≥25% (by Unit Entitlement) support for a “requisition” to the Executive Committee Secretary to convene a General Meeting of the Owners Corporation to review the documents and to consider a Motion to continue legal actions. If those actions are quoted (and they have to be) to exceed the lesser of an amount equivalent to $1K/Lot or $12,500 in total, then the Meeting needs to resolve to proceed or to knock a continuance of those legal actions on the head!
Just in case the quoted legal expenditure is less than the threshold (above), then you should include a Motion to restrict the delegations of your Committee and/or the Strata Manager such that the approval of legal actions/costs resides solely with the Owners Corporation.
There are more radical solutions available, but hopefully one of the above will work for you. I just hope you’re in NSW because every State and Territory is a little different legislatively, but the principles still apply.