The first seems like an odd variety of sweet potato. It has the same growth habit as sweet potato.

The next two have thick, succulent-lke leaves. The red one has purple berries.

The last one my grandparents use in stews. It has a slimy texture when cooked.

Thanks!

The second and third are respectively the white and red forms of Basella rubra (of which B. alba is a synonym), Malabar spinach.

The fourth is Corchorus olitorius, which goes by many different common names and is both a fiber crop and a green vegetable.