Party level depends on how you want us to plane-hop.
Using spells,
ethereal jaunt is 7th level, but only affects the caster. It also only goes to the Ethereal Plane.
Etherealness is 9th level and would affect at least five other beings plus the caster.
Astral projection is also 9th level, and would bring along at least eight warm bodies.
Gate, also 9th level, would take as many people as can cram through it while it's open.
But
plane shift, 5th level for a cleric (7th for wizards), lets a group of eight instantly travel to the plane of their choice. They just have to research how to reach it -- traditionally, a metal tuning fork is used in the spell, and the fork's tone and metal determine the destination. (There was a lengthy article in an old Dragon Magazine detailing it, if you want me to see if I can relocate it.) Eberron's planes would require you to create your own keys.
So, giving the party the means on their own, you'd need at least 5th level cleric spells which means a 9th level party at minimum.
If you want to use magic items, that opens up other possibilities. You could always simply put the required plane-hopping spell(s) on scrolls, but that's a bit pedestrian.
- A staff of passage can cast astral projection for two charges. (CL 17th, 170,500 gp)
- An amulet of the planes works like plane shift but if you blow the Intelligence check you go to a random location (or plane). (CL 15th, 120,000 gp)
- A cubic gate would have to have five of its destination planes set in advance, and it opens to random locations, so you'd end up with a bit of a "Sliders" vibe because each trip is taking a chance. (CL 13th, 164,000 gp)
- A well of many worlds works somewhat like a portable hole, except that every time you open it, it opens to a random spot on a random plane. It's a two-way gate, but every time you pick it up you don't know where it'll open next. (CL 17th, 82,000 gp)
And that's just the stuff from the SRD. This being Eberron, you could always make some sort of eldritch machine that creates gates -- sort of like a Stargate. You could make it where it automagically yanks travelers back after a certain time, so each trip would have a time limit. Or establish fixed gates on each destination plane, but that would require thinking about the strategic use of them.