Executive committee power

Surely one of the by-laws or part of the relevant state legislation is that all owners must be able to have reasonable use and enjoyment of the common property (or words to that effect). If you are denied access to the BBQ (common property) then that also is a breach of the by-laws. Surely the two cancel?! If you are still up carousing at 3 AM and keeping everyone awake, then you would have breached a valid by-law.

@Luke said:
 They also threaten a $550-$5500 fine for breach of by-law (which I know is wrong)

What are my rights? Any advice on any way to proceed? 

Actually the $5,500 fine information is here:

The up to $5,500 fine can happen when you ignore an NCAT order. http://www.flatchat.com.au/by-laws-and-breaches-the-options/

Your rights are to either abide by the OC by-laws or take the OC to mediation or to NCAT.

So if you think the OC is wrong, you certainly have the right to challenge them.

How to ignore idiotic strata by-laws.
If you do not plan to have a gathering of more than 4 people, or how ever many it is the by-law says, for at least another year then breach the by-law because all the OC can do  if you breach a by-law is send you a notice to comply which is little more than a form that says “you have been naughty so do not do it again for a year or we can drag you off to NCAT for a fine that could be as high as $550”.
Notice i say could be be as high as. Rarely do NCAT hit people for the full amount.

In a nutshell feel free to breach any by-law as long as you do not plan to do it again within a year; and that assumes you actually get sent a notice to comply (NTC) for a breach because it is only once you get the NTC that the clock starts on the one year you need to be good.
In fact keep breaching them until you get a NTC. What can the do?

They can do the above or the other option, more complicated option, the OC has is to seek an order against you and those orders have a slightly longer shelf life but they generally also have an expiry date. What the OC do in that case is the OC request mediation (you do not have to attend), then the OC make an application for an adjudicators order, the OC write a submission and then having spent $160 or so of the OCs money and spent some time on the paperwork the OC after about 4- 6 months from the start of the whole process hopefully get an order to their liking.

The second option is rarely undertaken and if it is undertaken then the matter is normally far more “criminal” than having a few friends over for a BBQ (gathering)

I find your situation very humorous. Just have the gathering and tell the OC “send me a NTC” and i will light next years BBQ with it; just make next years BBQ 366 days after you get the NTC.

For your reference:

45   How can an owners corporation enforce the by-laws?

(1)  An owners corporation may serve a notice, in a form approved by the Director-General, on the owner or occupier of a lot requiring the owner or occupier to comply with a specified by-law if the owners corporation is satisfied that the owner or occupier has contravened that by-law.

(2)  A notice cannot be issued under this section unless a resolution approving the issue of the notice, or the issue of notices for the type of contravention concerned, has first been passed by the owners corporation or the executive committee of the owners corporation.

(3)  Subsection (2) does not apply to the issue of a notice under this section by a strata managing agent if that function has been delegated to the strata managing agent in accordance with this Act.

Note. The Tribunal may impose a pecuniary penalty on a person for failing to comply with a notice under this section (see section 203).

You can find the form referred to in s45(1) here;
https://www.fairtrading.nsw.gov.au/pdfs/About_us/Forms/Notice_to_comply.pdf

and see the form says the OC must apply for the fine within 12 months of the notice. Note that is if you re-offend. That is not because you originally offended, you need to re-offend if the OC wish to pursue the fine.

172   Duration of order by Adjudicator

Except to the extent that the order otherwise provides, an order made by an Adjudicator under this Part (other than an interim order) ceases to have any force or effect on the expiration of the period of 2 years that commences on the making of the order.