Storing cast iron in the oven
Will this effect how the oven heats up/cooks food?

The greater thermal mass means the oven will take longer to heat up, which is undesirable if you want to cook quickly, but it will also lessen temperature fluctuations from opening the oven door or the heating element cycling, which can be desirable. The block of metal is performing one of the roles of a pizza stone in this regard.
Depending on where the heating elements in the oven are situated, the size of the oven and the size and positioning of your cast iron, it may impact how heat distributes, for example by 'shielding' food from a lower heating element, and blocking the flow of air. Each situation is likely to be different so it is hard to say whether this will be a serious impact in your case.

Will it harm the pans?

Very unlikely; your cast iron is designed to be happy at oven temperatures. If there is food residue on the pan you may find that repeatedly heating/burning it and letting it cool can make it very hard to clean off without a tough abrasive, so make sure you clean your pans thoroughly before storing them.
Similarly, the whole point of seasoning on a pan is that it is formed in high oven temperatures, so it should not be damaged by exposure to similarly high temperatures. As discussed in the answer here, seasoning can be damaged by high temperatures, with the temperature necessary varying depending on the seasoning itself. If your pans' seasoning has survived so far, I would not expect this to change with further time stored in the oven, but if you season a new pan and store it in the oven you should not be surprised if the seasoning is at times damaged as described in that question. (This is the point I am least confident about, so would be open to correction in the comments if it is from a reliable source.)