Does placement of antennas near other circuit components like inductors and crystal oscillators have an effect on the radiation efficiency and other performances of the antenna?
Metal objects near an antenna will have an effect on it, paticularly when the metal is in a direction that you want the antenna to radiate or when the metal is about a tenth of a wavelength or larger in size.
To add on to what throwaway18 said, you have to consider the polarisation that you wish your antennas to radiate in. Unless of course, if you plan to place your components under the ground plane, e.g. patch antenna, then you can worry less.