BESIDES POLITICS what does Elizabeth Taylor have in common with Sen. Edward M. Kennedy, Sen. Howard Baker, John Connally and Bob Strauss?

They all get their hair done by uni-sex stylist Harold ("Harry of K") Knight, who recently moved from the Madison Hotel to the Hyatt.

Knight still expects to be the next White House barber, although his chances don't look as good now as they did earlier when he was clipping three 1980 presidential contenders.

Kennedy could use someone around him on the campaign who is handy with a blow-dryer, says Knight. The senator refuses to learn to use one himself and frequently gets out of the shower with wet hair, runs a comb through it and goes before television crews with damp curls plastered to his head.

Knight wishes every politician paid as much attention to his crowning glory as the silver-maned Connally, who has locks lightened with "White Mink."

Or evangelist Billy Graham, who once summoned Knight for a comb-out before a prayer breakfast.

Taylor is Knight's favorite client, even though she did once get him in trouble with the Madison's Marshall Coyne when she started craving lamb chops under the dryer. When the hotel kitchen could not serve her in the barbershop because of health department regulations, Knight sneaked in and got them anyway.

Knight got caught and received a chewing out while she munched happily away.

No one's done a "Shampoo" movie about VIP barbers yet, but stylists have status in Washington. Henry Kissinger used to send a chauffeured car to transport Milton Pitts two blocks from his shop in the Sheraton Carlton across Lafayette Park to the White House.

They make good money. One of Knight's Saudi princes tipped him $500 and refused to take a refund when Knight offered him three $100 bills back, assuming he only meant to tip $200 as usual.

Knight could get rich selling the floor sweepings after he gets through shearing Ted Kennedy. All the ladies want locks of his hair and so far Knight has been giving them away on request.

Her typing may still be hunt and peck, but Liz Ray is working away on an Abscam novel about gambling and politics -- and sex, of course -- in and around Atlantic City.

Now living in New York for the past two years, Ray called superagent Irving Swifty Lazar in Hollywood recently to ask him to represent her.

He didn't remember who she was, until she said the words "Wayne Hays."

When President Carter decided he wanted to see the new Alan Arkin movie, "Simon," about an unscrupulous think-tank running wild, he had to wait. The Russian Embassy had borrowed the Motion Picture Association's VIP "freebie" copy . . . If diamonds are a girl's best friend, Phyllis Diller says she is now almost friendless. Due here May 8 for the White House News Photographers Association dinner, Diller reports her 29th jewelry robbery. Someone lifted her diamond "P" from a Chicago hotel . . . Carter-Mondale campaign chairman Bob Strauss could have bought the place for a pittance when he started renting his favorite Del Mar beach house in California 20 years ago. sNow it's costing him $650,000. But the owners are taking back a $350,000 first trust . . . A proud David Brinkley, celebrating his son Joel's Pulitzer Price for international reporting with a party at New York's "21." p

Clyde Litton, the plastic surgeon who sometimes plays tennis with Sen. Edward M. Kennedy, is accustomed to getting questions lobbed at him about the intricacies of various cosmetic surgical techniques.

Kennedy was fascinated with a description of lipectomy, the excision of fat, particularly in the abdominal area.

"The way I eat, you'd better reserve one of those operations for me once a year," said the senator.