Hammond organ clones with piano emulation?

Lots of keyboards have preset organ sounds, but if you're talking about what people call Hammond clones or clonewheels (because they clone the sound and operation of the original Hammond organs that used mechanical tonewheels), you need the ability to manipulate the levels of the individual drawbars, the 9 variable tone components that you use to sculpt the sound and create all the tonal variations as you do on the real thing.

Organs play best from unweighted actions, pianos play best from weighted actions. It sounds like the primary goal of the OP is the organ function, with the piano function secondary, so let's look at current models with unweighted actions. I've noted the ones that have real drawbars… the actual mechanisms vary, and some purists call some more real than others, but for these purposes, I include any that have the authentic look, shape, and spacing. In some cases, I've noted some key features or differences, but by no means all the important ones. I've included some references to their synth functionality since that was also mentioned in the thread.

Nord has a variety:

Electro 4 - the D version has real drawbars, the SW73 version has more keys, but you lose the real drawbars.

You may also still find some Electro 3 around, which (as you would guess) is an older version of the Electro 4. No real drawbars, and slightly lower quality (but still excellent) organ sound.

Stage 2 (73) - organ sound is again not quite as good as the 4 series, but still excellent (and better than many others here), and it does not have real drawbars. But unlike the Electros, they can play more than one sound at a time. They also have full synthesizers built in. (The Electros have some synth presets you can load into them, but you can't alter them the way you can on a real synth, nor can you play them very expressively since the Electro lacks even the rudimentary synth controllers of pitch bend and modulation.)

The Nords that do not have real drawbars use a simulation that uses up and down buttons and LED displays instead. Their overall design still tries to capture much of the organ ergonomics as drawbar models do (and non-drawbar models generally do not). I think that, as clonewheels go, Nord has the best piano sounds, though I don't think they play very nicely from Nord's unweighted actions.

Hammond has the SK1, and the SK2, the latter being the only two-manual option. Real drawbars. 73 and 88 key versions of the SK1 are coming out later this year. They also have a couple of basic synth sounds, albeit with no controls (not even pitch and modulation controls).

Roland has a variety:

VR-700 - real drawbars, and one of the best feeling organ actions around (and as a bonus, the action is better than most unweighted actions for piano, if you must play piano from an unweighted action). Some synth sounds, not much, but at least you have pitch and modulation controls.

VR-09 coming out probably in April - action expected to be not nearly as good as the VR-700, but piano/organ sound and functionality should be similar (though fewer keys). Full synth functionality, editable via iPad.

Jupiter 80 - not quite all the organ functionality of the VRs, but you do get drawbar control via a touch display, lots of other sounds and synth capabilities, and a nice action.

Jupiter 50 - similar to Jupiter 80, but without the touch display, drawbar settings have to be made through a menu. A lot of the 80's synth control function can be added with an iPad app.

Although the Jupiters and VRs both let you control organ sounds at the drawbar level, there are other aspects of the sound (overdrive, chorus/vibrato, etc.) which are handled better on the VRs (and most other clones). So from the Rolands, if you're focusing on organ, you'd probably prefer a VR to a Jupiter.

Korg has the Kronos and Kronos X 61, which includes their CX3 engine along with piano and a lot of other functionality, including full synth. They use faders instead of drawbars.

Kurzweil has the PC3K6, which includes their KB3 engine, piano, and lots of other functionality, including full synth. They use faders instead of drawbars. You may also find the PC361 around, which is the older version without sample memory. There are also 76 key versions (PC3K7, PC3) though the action is different, I think less good for organ, though some people find it a better compromise for also playing piano. There is also the PC3LE 6 and 7 which have that compromise keyboard, have a slightly lower end rotary speaker emulation, and use knobs instead of faders or drawbars. (They also make a scaled down version of the LE, the SP4, but you would need some kind of external control box to access its drawbar functions over MIDI.

Yamaha has nothing. The closest they come is the Motif XF with the optional Organimation or Organ Session library… that can give you drawbar style control, but even then, you only get independent control of 8 of them at a time… you can't get all 9, due to the fact that the Motif only has 8 faders, and just the general architecture of the machine. Also, these attempts to turn a Motif into a clonewheel, while clever in that they work at all, can exhibit various limitations such as limited polyphony or phase cancellation issues within the samples.

Casio has the XW-P1. It uses small sliders instead of drawbars, tone is a bit less authentic than most (with the rotary effect being especially lacking) and it is weak on some of the enhancements like chorus/vibrato and overdrive. And it's piano sound is nothing to write home about either. But it's cheap, light, has a surprisingly decent feeling action, and a nice synth section.

If you decide to go with a piano-oriented weighted action instead of an organ-oriented unweighted action, Nord, Kurzweil, and Korg make weighted versions of all the boards of theirs that I listed above. Of those, the Nord Stage 2 weighted action is probably the best adept at handling organ, the Kurzweil PC3 is probably okay too. Kronos, Nord Electro, and Kurz SP models would be less cooperative. Kawai also has a tonewheel mode in their MP6, and Roland has some of that functionality in some of their weighted boards as well, like the RD-700NX and possibly some others.

It's still best to get two boards with two actions. A lightweight weighted 88 board will be better for playing piano than any unweighted action, there are plenty to choose from, from the Yamaha P-35 on up. The forthcoming 24 pound Casio PX-5S looks especially nice. You can use these things with their own piano sounds, or to trigger what may be a better piano sound inside your organ board via MIDI (as you might if, for example, you were to choose an unweighted Nord for your organ board, since those boards also have such good piano sounds).

Finally, whatever you get can be augmented with other external devices. For example, if you get a board that doesn't have much synth functionality, and you happen to own an iPad, there are great iPad synths you can trigger from whatever keyboard you get. For that matter, the clonewheel organ built into the iPad's GarageBand program is quite nice itself.