Did you already diagnose your PCM with a scan tool and check your fluid level? Also, is the fluid clean - and not burned smelling? Will the transmission work in any other gears; reverse, park, neutral?

transmission cable must be broken. not allowing you to shift to the bottom of the transmission (gears 1 3 and 5)

not a problem my buddy had the same problem in his 5 speed

If the torque convertor was.nt all the way in when installed-possible broken pump gears-a common mistake when installing transmissions

Fuel filter-Possible stopped up cat... convertor

Have you checked to see if the cotter pin broke that holds your clutch together with the master cylinder? Follow the clutch up to the firewall and inspect it, the linkage shaft that comes out of the firewall has a "U" shape that goes around the back of the clutch. A pin feeds through these and is held in place with a cotter pin. Move the clutch and see if it is engaging the shaft of the master cylinder, if not then there is your problem but easily fixed.

Usually, this is an indication of a leaking transmission cooler tank in the radiator - may have a small leak. First step, have the cooling system pressure tested when the engine is cold - to determine if there is any leak.
If the radiator needs repaired, or replacing - try the 'Find-A-Shop' feature on this website, or try the many on-line auto parts sources, such as; www.RockAuto.com or www.autopartswarehouse.com for the replacement parts.

Research the used car reviews and price guides, also check the many on-line Honda Odyssey owners forums. The transmission quality / reliability is questionable - often failing without warning. Use the 'Estimate Cost' feature on this website to gain rough cost estimates for the rebuilding / replacement transmission.
Generally, any used vehicle quality and reliability is function of; previous manitenance history, mileage, and vehicle build quality.

Look for possible bad acuator on lower part of steering column or maybe the shift cable itself