I know that the 4 knobs are assignable.

There are two sets of four Assignable Knobs, you access them by pressing the [ASSIGN] button a second time. When lit Assign Knobs 1-4 are available, press [ASSIGN] again, it flashes to indicate Assign Knobs 5-8.

Are the four sliders assignable as well?

There are four sets of four Sliders, 1-4, 5-8, 9-12 and 13-16.
Each of the 16 Parts of a Performance has its own Slider. When “Part“ Control is selected (green) you can flip between [1-4/5-8] using the dedicated button.
Use [SHIFT] + [1-4/5-8] to select Part Sliders for Parts 9-12 and 13-16, respectively.

When “Element/Operator” is selected (green), the Sliders work as individual Oscillator Level for the 8 Oscillators per Part. AWM2 Oscillators are called Elements, and FM-X Oscillators are called Operators. You can flip the role of the Sliders from 1-4 and 5-8

That is, can I assign a particular MIDI control message to each slider?

Yes, Added in version 2.50 you can use the Knobs, Sliders, and Switches via USB-MIDI Port 2, as a Remote Control Surface for the following DAWs: Cubase, Logic Pro, Pro Tools, Ableton Live. You also have Transport Control and can assign Knobs, Sliders, and Front panel buttons to control your various computer-based Plug-ins.

They are assignable when the “Remote” is activated.

The Knobs, Switches and Sliders are used to generate messages designed so that if documented and played back to the MODX, they will recreate your exact performance down to the smallest detail. You don’t say what your application is, what are you attempting to control?