When enchanting items with anvils of Krong is there a limit to the number of enchantments allowed or number of times an item can be used with anvils? If there is, do the bonus enchantments from using more lutefisk at a lutefisk statue count towards that limit?
It is effectively unlimited (except probably by how many different stats are available).
When you factor in the possible results of using an Anvil of Krong on previously enchanted objects or the (currently bugged so it adds extra enchantments in some cases) "This Translation is All Wrong!" Archaeology ability it is possible to get items with lots of enchantments.
Here's a fun image demonstrating this, taken from a post on the official forum: