Hi guys, when I start my 98 Millenia S first time in the morning or when it sits for couple hours a cloud of smoke comes out from exhaust just for a few seconds and then clears up. Smells like it runs rich.

Any ideas of what might be the cause?

 

Well, if it's loosing oil, then it's likely oil leaking through a part of the engine.

It's an old car... They eventually stop working the way they used to.

Is it loosing oil?

 

The thing is that smoke doesn't smell like oil, it smells like the car is running rich. No the car is not loosing any oil.

 

Only on startup? OK, if smoke is blue and has an oily smell, it's oil, and since it's only on startup, that suggests it's coming down the valve guides. A static and dynamic cylinder compression checkup will determine if the problem is with one or more cylinders.
If the smoke is black and smells like a rich mixture, the cause may well lie with the evap. loop scavenging.
The purge solenoid and purge valve operate on startup to extract the fuel accumulated in the charcoal canister. If the canister has seen better days, there will be a pool of fuel in there which will be "slurped up" during the purge cycle when the engine is fired up, causing an initial burst of black exhaust.