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Renda vs. aluguel vs. aluguer

Word practice demo
The choice between renda, aluguer, and aluguel depends primarily on the regional dialect (European vs. Brazilian Portuguese) and whether the item being rented is a piece of real estate (immovable) or an object (movable).

Renda

A2
In European Portuguese (Portugal), renda is the specific word used for the periodic payment made by a tenant for housing, apartments, or land. Note that in Brazil, renda usually means income or revenue, rather than rent payment.
Já paguei a renda deste mês ao senhorio.
(I have already paid this month's rent to the landlord.)
Os valores da renda em Lisboa estão muito altos.
(The rent prices in Lisbon are very high.)
Eles receberam um recibo de renda após o pagamento.
(They received a rent receipt after the payment.)

Aluguel

A2
This is the standard term in Brazilian Portuguese for the payment made by a tenant for housing. In Brazil, aluguel is a versatile word that covers both the money paid for a property and the renting of movable objects like cars.
O aluguel do meu apartamento vence todo dia dez.
(My apartment rent is due on the tenth of every month.)
Estamos procurando uma casa com aluguel barato.
(We are looking for a house with cheap rent.)
O valor do aluguel aumentou muito este ano.
(The cost of the rent increased a lot this year.)

Aluguer

A2
Used in European Portuguese (Portugal), aluguer refers to the act of renting movable items, such as cars, equipment, or costumes. It is generally not used for housing payments (which is renda), whereas the Brazilian equivalent aluguel covers both contexts.
O aluguer de carros no aeroporto é muito prático.
(Car rental at the airport is very practical.)
Fizemos o aluguer de um fato para o casamento.
(We did a suit rental for the wedding.)
O contrato de aluguer da bicicleta dura apenas duas horas.
(The bicycle rental contract lasts only two hours.)

Summary

Use aluguel for housing payments in Brazil. Use renda for housing payments in Portugal. Use aluguer in Portugal when referring to renting movable objects like vehicles or equipment.