a barbecue party

[Ashiuhto]

Are the following sentences acceptable? Which is better?

(1) The Smith family had a barbecue party to celebrate the festival.
(2) The Smith family celebrated the festival by having a barbecue party.
(3) The Smith family celebrated the festival by barbecuing.

[bhaisahab]

Are the following sentences acceptable? Which is better?

(1) The Smith family had a barbecue party to celebrate the festival.
(2) The Smith family celebrated the festival by having a barbecue party.
(3) The Smith family celebrated the festival by barbecuing.

1 and 2 are OK.

[Ouisch]

In AmE, we don't often say "barbecue party", we just say "barbecue."

So, in AmE, instead of this:
(1) The Smith family had a barbecue party to celebrate the festival.
We would say:
The Smith family had a barbecue to celebrate the festival.

Instead of this:
(2) The Smith family celebrated the festival by having a barbecue party.
This:
The Smith family celebrated the festival by having a barbecue.

This sentence is fine:
(3) The Smith family celebrated the festival by barbecuing.

Some native speakers might expand the sentence a bit and be more specific about what food(s) were cooked at the barbecue:
The Smith family celebrated the festival by barbecuing steaks and corn on the cob.