The lodges are private clubs... community centers, but for members only. Many offer weekly activities: BBQs, bingo, poker, karaoke, etc, and almost all that I have seen have a nice bar (or two, in the case of my home Lodge). Some have full restaurant style kitchens, others may not.
Most will allow members to overnight in their lots for no cost (local laws allowing). Since most of these lodges have been around well before the local ordinances, many are grandfathered in to still allow camping and such even though the city/county forbids it. For instance, my home Lodge allows the Boy Scouts to camp here a few times each month. ROTC camps here too.
Most do not have hookups, but about 10% do ( a little planning will get you to one when you need it). They are primitive hookups in many cases (no sewer) and usually only have a few spots with hookups, but there are rarely anyone using them.
This past year I have visited numerous Lodges. I've watched the Super Bowl in Truth & Consequences, NM (full hookups) with a huge potluck meal, stayed a few weeks just outside of Glacier National Park (full hookups), and stayed many overnights in my a-to-b travels. They are safe places with no harassment from local law. I can go in and have a beer with people that instantly welcome me as their close friends and many have treated me out to dinner (and beer) on those 1-night stays.
Just walk into your local Lodge and ask them about info. They would be happy to give you the tour and answer any questions. My biggest fear was if they were religious or not. They ask only that you "believe in a higher being", but do not dictate which "being" that is. I have yet to see any prayers in the functions either. And, NO you do not need to wear antlers in the lodge
Each lodge may be different, but generally I have donated $10 per night (or $50 per week) for hookups, and half that for no-hookups. It is also $70 per year to be a member for the Moose (I assume the Elks are about the same). There are 2500+ Moose Lodges around the country and Canada, so you always have a "home" no matter where you are. And so far, everyone has treated me just like family from the moment I walk in the door to say hello.
You can read up on my Lodge experiences on my blog
And remember, it is all tax deductible too, so it comes right back into your pocket (kinda) each year.
http://www.mooseintl.org/public/default.asp - Main web page
https://secure.mooseintl.org/LodgeChapterLocator/default.aspx - find a lodge
https://secure.mooseintl.org/LodgeChapterLocator/CampRVReport.aspx?reporttype=rv - lodges with RV hookups