I might go to a party today and there will be veg pastries made by an Indian company Monginis.
When I searched for these pastries, I found that milk solids are used in these cakes. Are they vegan and should I eat them?
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Judging from the descriptions on the Monginis site, these pastries contain milk solids and therefore are not vegan. The name veg pastries is a bit misleading there, since it does not seem to have anything to do with veganism, but rather with whether there is egg used in the pastry or not. Whether you should eat them is upon you though and not something that others can help you with.
You might be fine with occasional "cheating" or be fine with smaller amounts of animal products in some foods or, on the other hand, you might be really strict about your eating (and possibly moral?) habits and will therefore decide to abstain from eating these cakes.
What I am saying is that there is not an universal right or wrong here; you need to make a decision that you will be most comfortable with. However you decide, enjoy the party :)