www.gsmworld.com shows those networks as 3G

Highly unlikely that you'll be able to use your existing 2G GSM handset
in Osaka. DoCoMo and Vodafone use different CDMA networks in Japan
(DoCoMo uses FOMA, Vodafone is CDMA 1X) for 2G.

Maybe get a UMTS phone.

You should be able to rent a WCDMA handset at the airport that will
allow you to use your GSM sim.

Certainly not with DoCoMo.  I am not sure of GSM availability in
Japan. Vodaphone in most of the world is GSM, but they are part owners
of CDMA systems in the USA.

The Japanese system is called PDC, and while it has a number of
technical similiarites to GSM, just as IS-136 has, there is no
interoperatbility that I am aware of, not to mention that the
frequency allocations for PDC are 'bizarre'. (it is in several
discontinuous pieces).

Does this mean it's possible to use

Been there, done that. So this is no gessing. There is no GSM in Japan.
Period. Your plain old tri or quad-band GSM handset will not work. What they
have in Japan is WCDMA-2100 3G (a.k.a. 3GSM) service from two carriers:
(Vodafone & DoCoMo) which can support SIM roaming with GSM carriers. You
will need a WCDMA-2100 handset to roam these carriers. You may be able to
rent one from your carrier before you go but you can also rent one from the
Vodafone Rental kiosk at the Osaka airport. It is on the top floor
(international departures) on the right hand side at the rear. After you
arrive (bottom floor) you will need to go all the way to the top floor and
go past the check-in counters to find them. When I checked a couple of years
ago they charged something like 1,000 Yen/day to rent a WCDMA handset. I
don't know if they still charge that much, but clearly it's not a good idea
for long-term roaming. I don't have the URL for Vodafone Rentals but if you
check www.vodafone.com and follow the links to "Japan" you should be able to
find it.