Advantages of a shovel (far right of picture) include availability, and the ease with which roots can be obtained (at least for shallow rooted crops). Disadvantages include the temptation to take large subsamples, increased site damage over smaller instruments, and difficulty of reaching the rooting depth of some crops.
Oakfield tubes (second device from the left in the picture) are approximately 1 inch in diameter and 12 to 18 inches in length. Although several manufacturers now make similar devices, the term Oakfield is in common use among nematologists, similarly to the way Xerox is used to refer to copying machines of many brands. These devices are excellent for obtaining soil samples to depths of approximately 3 feet (if soil texture and moisture are conducive), but provide only bits and pieces of roots which are hard to separate and process. Ten to 15 cores are typically required to obtain a one quart sample.
Soil augers (far left) are available in a variety of diameters and with several different tip styles designed for different soil types or conditions (e.g. sand or mud). Diameters of 2 to 3 inches are typically used by nematologists. With a new auger, it's not uncommon for the welds holding the lower part or bucket of the auger to the upper struts to break under the stresses of sampling. If you have the opportunity, have the welds strengthened prior to using the auger or take two to the field. A rubber mallet (not pictured), available from hardware stores, is typically used to pound the soil out of the auger. Advantages of an auger include the ability to sample in drier and heavier soil types than with an Oakfield tube, to sample deeper than easily possible with a shovel or an Oakfield tube, and to be able to obtain sufficient roots. Disadvantages of using an auger in situations in which an oakfield can be used would be the greater time and energy input, greater site disturbance, and the temptation to take larger subsamples than with an Oakfield. Similarly, greater time and energy input are typically required for an auger than for a shovel.
A Viehmeyer tube (second instrument from the right) is a similar diameter to an Oakfield tube but can be used to sample to greater depths. A pointed hammer (center of the picture) which can be very dangerous if not used properly is used to pound a Viehmeyer tube into the ground and often must also be used to pound it back out again. A rubber mallet is used to tap the side of the tube to help remove the soil.