I would like to know if making Oath in different bases will affect repair cost of Heart of the Wolverine charges.

Oath is usually made in Eth items to which its charges cannot be repaired.

Repair Cost = [ item_value * (max_dur/dur) * (128 / 1024) ]

So yeah, specially superior bases will make the repair cost extremely high compared to non-superior.

is there any formula for the repair cost of charges on items?

Chipped gem+Ort+Weapon

This is da wae

I've tested it with a hero editor character and the repair cost for different weapons such as broad sword, axe, flail is ~18k for 1 charge of heart of the wolverine (oath runeword).

The solution is: make a gold find barb, or, don't use your wolverine charges.

Decisions, decisions...