I've been to a few engagement parties as well as planned my own and from my experiences, these parties tend to be in the evening and are either a dinner/cocktail party at a home or party room at a restaurant. For mine, we had a champagne party and served chocolate covered strawberries and chocolate mousse in wine glasses. I hung and draped white drapes in various hallways and areas of the entry way and living room,had lots of candlelight, and Frank Sinatra type music. My theme was "romance". We did an engagement toast and then mingled with each other. I also set up a table with a few hors 'devours like deviled eggs with caviar,pimento cheese finger sandwiches,cucumber and cream cheese finger sandwiches,stuffed mushrooms,stuffed jalepenos,and spinach artichoke dip.
My invitations had our engagement picture in the front ( i made my own invitations from shutterfly.com) and on the inside I simply wrote," Announcing the engagement of "my full name" and "his full name". Join them as they celebrate their decision to grow old together". Then I put the place,address,attire,and time.
I use shutterfly a bunch for thank you cards and invitations. If you don't have an official engagement picture of them, you can use a cute picture of the two of them.
If you are going to throw your friends party in your backyard, perhaps you can do something a little different that a standard "bbq" and do a hawaian luau party. Party City has a bunch of cute things for theme decorating. You can play reggae music,get those hawaian lai things, tiki torches, and serve frozen pina coladas or daquaris with little umbrellas. You can grill chicken and beef and make little hawaian skewers with pineapple. I love party planning! Good luck. :)