When it comes to rehearsal dinner invitations, it is perfectly acceptable for the bride and groom to invite their wedding party and immediate family by word of mouth. It is also acceptable to send written invitations. The larger and more formal the rehearsal dinner, the more likely that invitations will be sent.
The big question is whether written or verbal reception dinner invitations will assure that your guests RSVP in time. If the bride is in close touch with her extended family and fairly well-organized, it may be simplest to call her guests, invite them, discover whether they will come and arrive at the total number. The groom then does the same with his attendants and you are all set.
If this approach makes you nervous, go ahead and send written invitations. Make sure the invitations include clear instructions on how to RSVP, as well as the "due date." If you are the hosts, issue the invitations in your own name.
Match the formality of the invitation to the formality of the party. For a formal party, you can order formal invitations from the same catalogs that stock wedding invitations and you can "request the pleasure of your company at a rehearsal dinner for…" the happy couple.
For the more usual rehearsal dinner, you can use very attractive fill-in- the-blank invitations available at most stationery stores and museum card shops. Use any wording you like - clarity is usually better than cleverness. You can even simply write a personal note on your own stationery or on attractive note cards. Don't worry that people who don't recognize your name won't open the invitation card. Every direct mail marketer knows that no one can resist opening a handwritten envelope that's the size and shape of a greeting card.
While the wedding toast to the bride or to the happy couple is traditionally done with champagne, toasts at all other parties can be done with any drink at all, including non-alcoholic drinks (even the wedding toast does not positively have to be champagne - it is a tradition rather than a rule of etiquette.)
Your duties as host do not require you to serve alcohol at all, if you do not wish to. It is polite and acceptable to serve a limited range of alcohol (perhaps just red and white wine) and to stop pouring after every social drinker has had a glass or two, as long as you continue to serve water and non-alcoholic beverages.
Since the rehearsal dinner is the prelude to a long and stressful wedding day, it's very appropriate to skip or limit alcohol and to end the party early.
If you want to encourage toasts without implying heavy drinking, consider serving generous amounts of bubbly non-alcoholic beverages, from carbonated water to sparkling cider. You'll give the party "sparkle" without "kick."