@tanguatlay,
A party of women was doing several things in the town.
The above sentence is the correct one.
The use of the word 'were' cannot be applied here. In order to use 'were' the sentence would need to have been written 'Women were doing several things in the town.'. Or even, 'Parties of women were doing several things in the town.'
Both of the above refer to more than one. Women is more than one and parties is the plural of party, so, here too there would be more than one.
The word 'were ' is used for situations where more than one is indicated.
Again, 'A party of women ' refers to a group. One group. Therefore it is singular and uses 'was'.