Wish you luck and success. They're a bit old to straighten now, but if you feel you really need to, you'll have to dig a trench about 3ft (1M) away from the trunk, all around the tree, and down several feet.
The side where the tree leans away from will need some soil removed lower down.
The side the tree leans towards will need the roots either teased out somehow or trimmed. Avoid cutting thicker roots - tease them out.
Some more soil at the other 2 sides will need some shifting but you can now carefully work the tree back to an upright position - but not pushing on the trunk which would probably snap. You'll have to tip the soil ball itself.
Once upright, you'll need to fasten wires/string/rope encased in old hosepipe strips, enough to protect the tree bark, fasten, then fasten the other end to very secure stakes just outside the 3 ft (1M) trench. To stake them in the soil ball will only chop and kill existing roots, and not have anything really secure.
When all is roped and staked, water the trench really well with a bit of transplant solution added to the water, then fill in with compost or soil mixed with aged manure to encourage new feeder root growth. And keep fingers crossed.
Water well very regularly this season until you're sure the shift has taken.
BTW - the big tap roots all the trees will have formed should not be severed. This type of shift will only give them a slight kink which they don't mind. Cutting them will likely kill trees this old. A shovel/spade is no match for those big specialized machines that move trees.
Best of luck!