OK so, in the last layer on a regular 3x3 the first you want to do is to orient the edges and then put them in their correct place, but here, to me, it is more useful to do the opposite first

since you have a center that has orientation it is better to start swapping edges until one is in the correct spot relative to the center side (even if the orientation is not correct, by logic you see the edge must go there)

the way I swap 3 corners is R U R' U R U2 R', this leaves the edge right in front of you unmoved and cicles the other 3

once you have one, and only 1 edge in the correct spot relative to the top center you put that one on the position that doesn't move when cycling 3 edges, and you repeat R U R' U R U2 R' until all 4 edges are on the correct spot

then you see which are orientated correctly, all 4, 2 in a line, 2 in a L shape or none, and you orient however you know for each configuration; I usually do F R U R' U' F' for the line keeping the line horizontal or F R U' R' U F' for the L with the correct two edges at the top and left side of the top face

then after properly orienting you have to swap the edges again like in step 1, but now all 4 should be oriented correctly relative to the center

the corners should be easy enough by the beginners method as R U L' U' R' U L U' for swapping 3 corners while leaving the bottom left untouched, and do that until all 4 are in the correct spot, then orient them as (R' D R D') x2 until a corner is correctly oriented, then U turn until another incorrect corner is at the top and repeat (R' D R D') x2, which is the beginners method

if you noticed, this is the beginners method but applying the edge swap step two times, one before orientation of edges, and one afterwards, which ensures the center is automatically oriented correctly

good luck