Learn more about the Player Search System (PSS) here:
http://serebii.net/xy/pss.shtml
PSS is basically the main system for online communications, mainly battling and trading.
You can trade between a DS Lite and a 3DS.
BUT you
CANNOT trade between generations. So you can only trade between DPPt and HGSS. Then BW and B2W2 only.
To transfer your Pokemon from Gen 4 (DPPt/HGSS) to Gen 5 (BW/B2W2), you must use the
PokeTransfer.
To transfer Gen 5 to Gen 6, you must use the 3DS Apps:
PokeTransporter and
PokeBank.
All Pokemon are obtainable between XY and ORAS alone. All unobtainable Pokemon in XY are found in ORAS.
The only Pokemon you'll really miss out are version-exclusives (if you don't trade with others or don't own both versions) and event Pokemon.
GF made sure that almost every Pokemon is accessible in one generation alone.
DS/DS Lite/DSi systems will be obsolete soon. Even WiFi features of Gen 4 and 5 have already been cut off. So, you're left with just local communications.