I'd like to give some insight to this one. I think it's a interesting topic of the Portuguese Discovery Age, at the time of the earliest contacts between Europeans, Americans, Sub-saharan Africans and many Asians.
The Portuguese were as exotic to the people they encountered as they were to them. What kind of impression such newcomers and their strange apparatuses caused we can gather from two sources: what the natives wrote about the Portuguese, and, in case they were a non-literate culture, what the Portuguese wrote about themselves. Reactions were as different as people were disparate. The earliest perceptions tended to be initially formed along the lines of what the beholder was already familiar with, and would try to fit the Portuguese into that view, before a more accurate picture could be rationalized of what exactly they were seeing.
For example, in his Navigations, the Venetian Alvise Cadamosto recounted from the time he served aboard one of the caravels of Prince Henry the Navigator, that some people in West Africa though Portuguese caravels were some sort of huge, tameable seabird, their white sails looking like open wings. Bag-pipes were also a novelty to the Jalofo people, and since they were made with goat-skin, they though the white men had before them actual singing animals. Nor did they have any use for wax for example, even though they harvested honey. According to Cadamosto, it was the Portuguese that taught them to make candles.
Relations in West Africa were mostly mundane for most of this time, European presence being extremely limited to a few sea-side settlements for the purpose of trade. In Asia the impact was much more spectacular, because the Portuguese contacted many more and more literate cultures, and with much more varied interaction, from peaceful trade to brutal conflict of far-reaching consequences.
In the island of Ceylon, an oral tradition from about 1585 was recorded in the royal chronicle called the Rajavaliya, that read as follows:
A Ship set out from Portuguese territory in India in the year of 1522 [sic] of Our Lord Jesus Christ [the writer was a Christian Sinhalese], and traversing the immeasurable ocean without harm through the power of God/the Gods, arrived at the harbour of Colombo. The people who were at the port, having seen the ship reported thus to King Parakramabahu: there is in our port of Colombo a caste of people very white in colour and of great beauty; they wear jackets and hats of iron and pace up and down without resting for a moment. Seeing them eat bread and grapes and drink arrack, they reported that these people devoured stones and drank blood. They said that these people give two or three pieces of gold or silver for one fish or lime. The sound of their cannon is louder than thunder at the end of the world. Their cannon balls fly many leagues and shatter forts of stone and iron These and countless other details were related to the king.
In some places, like Cortez in central America, the circumstances of the arrival of the Portuguese coincided with ancient local legends. The Portuguese chronicler João de Barros recounts in his Decadas da Ásia about the arrival of Francisco Serrão to the Moluccas in 1512:
E como em todalas partes commummente vemos andar entre o povo umas esperanças futuras de bem ou mal, que há de sobrevir à terra, onde cada um vive; assi havia uma opinião entre a gente daquelas Ilhas, que a elas haviam de vir uns homens de ferro de mui remotas partes do Mundo, os quaes haviam de fazer ali morada; e estenderia por tôdas aquelas Ilhas, a qual opinião por o poder e, e fôrça deles o reino de Ternate se diziam proceder d’ElRei Boleife quási que a denunciavam em modo de profecia aos seus vassalos. Donde, quando ele vio Francisco Serrão ante si armado de umas armas brancas inteiras, acompanhado dos outros Portuguezes também armados das armas que tinham, levantou as mãos dando louvores a Deus, pois lhe mostrara ante da sua morte os homens de ferro, em cujas forças estava a seguridade de seu reino, e por cujo favor os seus descendentes haviam de permanecer por muitos anos com título de reis daquela terra
[...] And like in many parts, we witness among the people some future hopes of good or evil, that shall befall the land where each lives. Likewise the people of those islands believed that one day men of iron would settle there, and across all those islands, regarding whose power and strenght in the kingdom of Ternate king Boleife told it nearly like a prophecy. Thus, when he saw before him Francisco Serrão armed in a full suit of armour, accompanied by the other Portuguese likewise armed with their arms and armour, he raised his hands praising God, for showing him the men of iron while he lived, by whose forces the safety of his kingdom was assured, and by whose favour his descendants would remain as kings of that land for many years."
Like most inhabitants of the spice islands, the Ternateans were essentially an archaic tribal society; but Portuguese steel armour was not the only thing that struck an impression in such a culture: the then captain of Portuguese Malacca, Rui de Brito Patalim, reported in a letter to King Manuel in 1514 that the large, pitch black Portuguese carracks bristling with powerful cannon intimidated the peoples of insulindia (and for that very reason recommended their use, instead of chartering local merchantships).
Moving on to the "great kingdom of China", the situation was a bit different. The Portuguese reached China in 1513 but, long story short, were eventually banned after a number of diplomatical blunders when trying to establish trade, and a naval confrontation in the Pearl River Delta in 1521 put them in the same category of Japanese wako pirates. Far from being excluded effectively , trade simply moved underground to the world of smugglers. Nevertheless, the Chinese became aware of the Portuguese and realized the formidable potential of their armament.
In 1523, the haitao of Kwangtung Wang Hung reported to Emperor Jianjing:
The Folangji ["Franks", Portuguese] assumed such ferocious and rude behavior simply because they possessed cannon and ships of such kind. Their cannon are unsurpassed by any weapons that we know from ancient ages.
The Portuguese were equated as pirates, and this raised some alarm among the Chinese, who feared the Portuguese might return for some future incursion or retaliation. The Portuguese fleet in 1522 was small, about 6 vessels. It was deduced that 100 war junks were necessary to adequately defend the coastline as precaution.
Relations with the Portuguese eventually normalized and they were allowed to settle in Macau, after their services had been requested to clear a pirate stronghold where Macau was. Though treated with usual contempt, in 1569, a censor of the Ming court Chen Wute reported somewhat dramatically:
The Folangji were more ferocious in nature and more ingenious in the use of armaments than even the wako. Last year the bandit Tsang, with his full force attacked them [at Macau], who numbered less than a thousand but Tsang had to withdraw to a distant place having suffered heavy casualties in the encounter. We ought to learn about their strenght [of the Portuguese] from this.
The Chinese did manage to capture, reverse engineer a number of light Portuguese breech-loading cannon, and built a few of their own, but never achieved the technical quality of the Europeans. In time the Ming would even call upon Portuguese military aid to help against the invading Manchus.
Sources:
Alvise de Cadamosto: Viagens de Luís de Cadamosto e de Pedro de Sintra, in Portuguese, 1988 edition.
João de Barros: Décadas da Ásia in Portuguese, 1983 edition, Volume IV
John Villiers: East of Malacca: Three Essays on the Portuguese in the Indonesian Archipelago in the Sixteenth and Early Seventeenth Centuries 1985
Chandra R. da Silva: Portuguese Encounters With Sri Lanka and the Maldives – Translated Texts From the Age of Discoveries, 2009
Anthony Disney: Historiography of Europeans in Africa and Asia, 1450–1800 1995.