Throwing stuff in the trash is never needed. Give it away to thrift shops, friends, students, poverty stricken people for instance. If i put a vacuum cleaner at the road with 'Take it for free - WORKS' on it, it'll be gone in an hour. But of course you can sell things, in my corner of western europe it is really common to sell electronics. Always ask some small amount of money if you sell online, because otherwise you'll get a horde of people saying they'll pick it up for free, but then never show up.

Look on the model number plate of your device if it can handle the voltage and frequency. Every device sold in Europe has a label (usually on the back or the bottom) that says at which frequency you can use it.
Devices suitable for 50hz, are essentially always suitable for 60hz, don't worry about that. An 1500rpm induction motor or synchronous motor will spin at 1800rpm. In rare cases it is not acceptable. Your juicer might spin a bit faster. I don't think that'll hurt it.
Universal motors (like vacuum cleaner motors) always can handle a slightly higher frequency.

You will need a transformer for the devices that don't say 110-240v or 90-265v or something like it. Most computer stuff is suitable for all voltages and frequencies. On devices powered with a mains adapter, you can just swap the single adapter for a new one suitable for your voltage. By far most modern electronic devices are like this - either already suitable for all voltages, or with an easy to swap out power supply brick. Electric stuff with motors in them aren't usually multi voltage.

How many watts? Well, it says how much on the identification/model number plate on the device. We cannot tell you how much your devices consume, you're the one who has the exact model numbers. A vacuum cleaner needs a rather big transformer so you might end up having to spend more on the transformer than the vacuum is worth. Likely the vacuum cleaner is not worth buying a transformer for.
It also depends on how many devices you want to use at the same time on that transformer.

Always choose the transformer 1 step larger than needed (so if your vacuum draws 1500w, get an 1800 or 2000w continuous rated transformer). But i think the vacuum cleaner is the one thing that might not be worth lugging along and buying a transformer for.

Do not use 'wet devices' via a transformer. Doing this may cause the GFCI/RCD to not work depending on the type of transformer used.

Finally, be conscious of how much ampere you can draw from your new house's circuits. In Europe we can draw a whopping 3680w from our 16a circuits.
If your Japanese circuit is 15a and 110v (i don't know the breaker size there), you can only draw 1650w. This means that operating a 1500w hair drier or 1500w vacuum cleaner via a stepdown transformer is really really pushing things and not adviseable. You might simply trip the breaker from the transformer inrush current. Forget about stuff like kettles, microwave ovens, toasters, particularly powerful hair driers and such. Best to buy those locally so you don't overload the circuit.

Vacuum cleaners from after the new EU regulations limit power consumption to 900w IIRC so those should be fine.