Michael,
There are 3 ways I know of to do it do it. First break it down. Each time you see a semi-colon (in this case) or comma you are working with different tract or portion of the section.
E/2 NE/4 NE/4; SW 4 NE/4 NE/4; SW/4 NW/4 NE/4; N/2 S/2 NE/4
Method 1
E/2 NE/4 NE/4 = 1/2 x 1/4 x 1/4 x 640 (or .5 x .25 x .25 x 640) = 20
SW/4 NE/4 NE/4 = 1/4 x 1/4 x 1/4 x 640 (or .25 x .25 x .25 x 640) = 10
SW/4 NW/4 NE/4 = 1/4 x 1/4 x1/4 x 640 (or .25 x .25 x .25 x 640) = 10
N/2 S/2 NE/4 = 1/2 x 1/2 x 1/4 x 640 (or .5 x .5 x .25 x 640) = 40
20+10+10+40 = 80
Method 2
The third one may be easier to follow:
E/2 NE/4 NE/4 160/4 = 40 40/2 = 20
SW/4 NE/4 NE/4 160/4 = 40 40/4 = 10
Reading right to left, the NE/4 a ¼ of the section (640) so it is 160. Then the next NW/4 shows it is ¼ of the NE/4 so ¼ of 160 which is 40, the next SW/4 shows it is ¼ of 40 or 10 acres.
SW/4 NW/4 NE/4 160/4 = 40 40/4 = 10
N/2 S/2 NE/4 160/2 = 80 80/2 = 40
20+10+10+40 = 80
Method 3 plot it to see it visually,
E/2 NE/4 NE/4 Peach
SW 4 NE/4 NE/4 Blue
SW/4 NW/4 NE/4 Green
N/2 S/2 NE/4 Grey
Each of the smallest blocks represents 2.5 acres. 32 blocks * 2.5 = 80
or the next size larger blocks represents 10 acres.
All of this is for the standard 640 acre section. There are many cases where a section is not actually 640 acres. The ones you reference, Sections 27, 35, and 36 in Township 5S-1W in Carter Co, Oklahoma are all 640 acres each.
Here are a couple of more documents that might help.
BLM Load Record Overview
OSU Legal Land Descriptions in Oklahoma
Dave,
Please correct/enhance/criticize as needed.