Note: these comments reflect my personal experiences and opinions. I'm sure everyone's reactions to grief are somewhat different and what I want might not be what everyone else wants when they've lost a loved one (or two).
Since my sister and grandmother died last month, I've dealt with a lot of people's reactions to such awful news. Most people don't know how to react or what to say, which is understandable. I'm not sure I'd know what to say to me either.
Still, I appreciate it if you say something. It is awkward if you don't acknowledge it. You can just say you're so sorry to hear about my loss, even if that sounds generic. I don't care. Generic is better than nothing.
Yesterday on Facebook I was IMd by the younger brother of one of my high school friends. He is the same age as my sister and they dated for a minute in middle school. He asked me how I'm doing but didn't mention my sister, so I was in the awkward position of trying to figure out if he even knew. I thought he'd heard through the grapevine, but I hadn't received any form of condolances from anyone in his family so I wasn't sure. I finally brought it up but I wish he had just said something rather than beating around the bush. I guess her death hit him pretty hard even though they hadn't talked in years.
I think I'd also rather someone say something even at the risk of being rude. Some people have said unhelpful things to me, like Herb. Even if it doesn't come out quite right, I know the sentiment is there and they have acknowledged my loss.
Some have even been rude to the point of humor. When I was at the doctor a few weeks ago I explained to the nurse that I was there to talk to my doctor about my risk of blood clots in light of my sister's death. The nurse said she just lost her grandmother and was having a very difficult time. I said I also lost my grandmother the day before my sister, and she said, "Wow, here I am thinking my life is so horrible and feeling sorry for myself, and then I hear about you!" I just sighed and nodded, but inside I was laughing. I think what she was trying to say is that we're not alone in our tragedies- and it could be even worse. I think about that sometimes. It could've been worse. I'm glad if this tragedy helps you keep your life in perspective, but saying something generic would be more polite.
I have also greatly appreciated the emails, phone calls, cards and plants I've received expressing sympathy. I never really understood why people sent flowers to funerals, but now I think it's more important purpose is to support and comfort the friends and family members. Snail mail sympathy cards are still trickling in 6 weeks later. I don't think it will ever be too late for me to receive a sympathy card.