All modes can be used. But for bright targets, observations are limited to specific filters, subarrays, regions of the target planet, or spectral intervals.
James Norwood and colleagues wrote a paper on this topic, although the full answer is complicated because of the "subset of the instrument modes" part. The simplest answer to understand is for the imager, NIRCam:
In this plot, brightness of the planets as a function of wavelength is shown as colored curves, while little black lines show the filter bandpasses and saturation limits. So, any colored segments above the black lines mean that particular target would be saturated. This gives a rough idea of which filters can be used in the imager at these planets, but these values can vary depending on parameters like what part of the planet is imaged, whether a smaller or larger subarray is used (affecting minimum readout time), and even things like scattered light from Saturn's rings (which can be much brighter than the atmosphere at some of these wavelengths). Also, the sensitivity estimates for NIRCam were revised after the Norwood++2016 paper, and further revisions will come from in-flight testing.
The Norwood++2016 paper contains similar figures for some of the spectroscopic modes, where additional complications arise. A spectrum could be saturated at some wavelengths, but not at others, so would that observation be considered successful, partially successful, or unsuccessful?
Space Telescope Science Institute also put together a collection of nice 2-page JWST science flyers---a lot catchier than the Norwood++2016 paper---that cover what can/will be done by JWST for the targets mentioned in the original question:
The Mars flyer shows some pretty neat tricks. Target is too bright? Observe its night side!