broad, thick, wide
narrow, spaghetti (esp. AmE), thin
tight
loose
adjustable, detachable, removable, Velcro™
The bag comes with a removable shoulder strap.

leather, nylon, etc.
elastic, padded
carrying (esp. AmE), safety
a portable radio with a carrying strap

ankle, chest, shoulder, wrist, etc.
bra, guitar, watch, etc.

buckle, buckle up, do up, fasten
unbuckle, undo, unfasten
tighten
loosen
adjust
attach, clip on, fit
He clipped on his safety strap.

be fitted with
The camera was fitted with a strap.

on a/the strap
His binoculars were on a strap around his neck.

strap across, strap around, strap round (esp. BrE), etc.
She had a wide leather strap around her wrist.

safely, securely
firmly, tightly
down, in, on
He strapped his gun belt on.

around, round (esp. BrE)
His money belt was securely strapped around his waist.

in, into
Make sure that the child is strapped tightly into the seat.

to

Strap is used with these nouns as the object:
bomb