If ω is not a constant,
Phase noise L(Δω) ∝ ω^2
ω^2 = 1/LC
So L(Δω) ∝ 1/LC
If ω is a constant, LC must be a constant, because the Q of inductor is less than that of varactor, larger varactor means larger Q, then the phase noise is inversely proportional to the varactor capacitance.
For more details, you can read this book: Thomas Lee, The Design of CMOS Radio-Frequency Integrated Circuit.
About the mosfet, if it is parallel in the LC tank, it can be seen as a current noise source, inoise^2=4KTgm∝W/L the thermal noise is inversely proportional to the length.
If it is serial, it can be seen as a voltage noise source, vnoise^2=4kTR∝L/W, then the thermal noise is proportional to the length.